EDUC 

LIBRA 


THE  LIBRARY 

OF 

THE  UNIVERSITY 
OF  CALIFORNIA 

Education 

GIFT  OF 

Mrs.  T.  M.  Dunn 


N 


ON 


THE  CONNECTION 


THE   PHYSICAL   SCIENCES, 


BY   MARY   SOMERVILLE. 


From  tUa  Seventh  Loinioo  Edition. 


TWO 

NEW    YORK:  ¥ 

HARPER   &   BROTHERS,  PUBLISHERS, 

82  CLIFF    STREET. 

1846. 


Education 
Add  fii 

GIFT 


u 


PJIEFACE. 


THE  progress  of  modern  science,  especially 
within  the  last  few  years,  has  been  remarkable  for 
a  tendency  to  simplify  the  laws  of  nature,  and  to 
unite  detached  branches  by  general  principles.  In 
some  cases  identity  has  been  proved  where^  there 
appeared  to  be  nothing  in  common,  as  in  the 
electric  and  magnetic  influences ;  in  others,  as 
that  of  light  and  heat,  such  analogies  have  been 
pointed  out  as  to  justify  the  expectation  that  they 
will  ultimately  be  referred  to  the  same  agent,  and, 
in  all  there  exists  such  a  bond  of  union,  that  pro- 
ficiency cannot  be  attained  in  any  one  without  a 
knowledge  of  others. 

Although  well  aware  that  a  far  more  extensive 
illustration  of  these  views  might  have  been  given, 
the  Author  hopes  that  enough  has  been  done  to 
show  the  Connection  of  the  Physical  Sciences. 

In  order  to  keep  pace  with  the  progress  of 
discovery  in  various  branches  of  the  Physical 
Sciences,  this  book  has  been  carefully  revised. 


076 


CONTENTS. 


INTRODUCTION      .          .          .'," '     .    ~  '   /.  "7-  "     ,          .          •          .          Pag«  1 

SECTION  I. 

Attraction  of  a  Sphere — Form  of  Celestial'Bodies — Terrestrial  Gravitation 
retains  the  Moon  in  her  Orbit — The  Heavenly  Bodies  move  in  Conic 
Sections — Gravitation  proportional  to  Mass — Gravitation  of  the  Particles 
of  Matter— Figure  of  the  Planets— How  it  affects  the  Motions  of  their 
'  Satellites — Rotation  and  Translation  impressed  by  the  same  Impulse- 
Motion  of  the  Sun  and  Solar  System  4 

SECTION  II. 

Elliptical  Motion — Mean  and  True  Motion — Equinoctial — Ecliptic — Equi- 
noxes— Mean  and  True  Longitude— Equation  of  Center — Inclination  of 
the  Orbits  of  Planets — Celestial  Latitude — Nodes — Elements  of  an  Orbit 
— Undisturbed  or  Elliptical  Orbits — Great  Inclination  of  the  Orbits  of 
the  new  Planets — Universal  Gravitation  the  Cause  of  Perturbations  in 
the  Motions  of  the  Heavenly  Bodies — Problem  of  the  Three  Bodies — 
Stability  of  Solar  System  depends  upon  the  Primitive  Momentum  of  the 
Bodies 8 


SECTION  in. 

Perturbations,  Periodic  and  Circular — Disturbing  Action  equivalent  to 
three  Partial  Forces — Tangential  Force  the  Cause  of  the  Periodic  Ine- 
qualities in  Longitude,  and  Secular  Inequalities  in  the  Form  and  Position 
of  the  Orbit  in  its  own  Plane — Radial  Force  the  Cause  of  Variations  in 
the  Planet's  Distance  from  the  Sun — It  combines  with  the  Tangential 
Force  to  produce  the  Secular  Variations  in  the  Form  and  Position  of  the 
Orbit  in  its  own  Plane — Perpendicular  Force  the  Cause  of  Periodic  Per- 
turbations in  Latitude,  and  Secular  Variations  in  the  Position  of  the 
Orbit  with  regard  to  the  Plane  of  the  Ecliptic — Mean  Motion  and  Major 
Axis  Invariable — Stability  of  System — Effects  of  a  Resisting  Medium — 
Invariable  Plane  of  the  Solar  System  and  of  the  Universe — Great  Ine- 
quality of  Jupiter  and  Saturn 12 

SECTION  IV. 

Theory  of  Jupiter's  Satellites — Effects  of  the  Figure  of  Jupker  upon  his 
Satellites — Position  of  their  Orbits — Singular  Laws  among  the  Motions 
of  the  first  three  Satellites— Eclipses  of  the  Satellites— Velocity  of  Light 
— Aberration — Ethereal  Medium — Satellites  of  Saturn  and  Uranns  26 


VI  CONTENTS. 

9  SECTION  V. 

Lunar  Theory — Periodic  Perturbations  of  the  Moon — Equation  of  Center — 
Evection — Variation— Annual  Equation — Direct  and  Indirect  Action  of 
Planets— The  Moon's  Action  on  the  Earth  disturbs  her  own  Motion- 
Eccentricity  and  Inclination  of  Lunar  Orbit  Invariable — Acceleration — 
Secular  Variation  in  Nodes  and  Perigee — Motion  of  Nodes  and  Perigee 
inseparably  connected  with  the  Acceleration — Nutation  of  Lunar  Orbit 
— Form  and  Internal  Structure  of  the  Earth  determined  from  it — Lunar, 
Solar,  and  Planetary  Eclipses— Occultations  and  Lunar  Distances — Mean 
Distance  of  the  Sun  from  the  Earth  obtained  from  Lunar  Theory — Abso- 
lute Distances  of  the  Planets,  how  found  ....  Page  33 

SECTION  VI. 

Form  of  the  Earth  and  Planets — Figure  of  a  Homogeneous  Spheroid  in 
Rotation — Figure  of  a  Spheroid  of  Variable  Density — Figure  of  the 
Earth,  supposing  it  to  be  an  Ellipsoid  of  Revolution — Mensuration  of  a 
Degree  of  the  Meridian — Compression  and  Size  of  the  Earth  from 
Degrees  of  Meridian — Figure  of  Earth  from  the  Pendulum  .  43 

SECTION  VII. 

Parallax — Lunar  Parallax  found  from  direct  Observation — Solar  Parallax 
deduced  from  the  Transit  of  Venus — Distance  of  the  Sun  from  the 
Earth — Annual  Parallax — Distance  of  the  Fixed  Stars  .  .  51 


SECTION  VIII. 

Masses  of  Planets  that  have  no  Satellites  determined  from  their  Perturba- 
tions— Masses  of  the  others  obtained  from  the  Motions  of  their  Satellites 
— Masses  of  the  Sun,  the  Earth,  of  Jupiter,  and  of  the  Jovial  System — 
Mass  of  the  Moon — Real  Diameters  of  Planets,  how  obtained — Size  of 
Sun — Densities  of  the  Heavenly  Bodies — Formation  of  Astronomical 
Tables — Requisite  Data  and  Means  of  obtaining  them  .  .  .  54 


SECTION  IX. 

Rotation  of  the  Sun  and  Planets — Saturn's  Rings — Periods  of  the  Rotation 
of  the  Moon  and  other  Satellites  equal  to  the  Periods  of  their  Revolu- 
tions— Form  of  Lunar  Spheroid — Libration,  Aspect,  and  Constitution  of 
the  Moon — Rotation  of  Jupiter's  Satellites GO 


SECTION  X. 

Rotation  of  the  Earth  invariable — Decrease  in  the  Earth's  Mean  Tempera- 
ture— Earth  originally  in  a  State  of  Fusion — Length  of  Day  constant — 
Decrease  of  Temperature  ascribed  by  Sir  John  Herschel  to  the  Variation 
in  the  Eccentricity  of  the  Terrestrial  Orbit — Difference  in  the  Tempera- 
ture of  the  Two  Hemispheres,  erroneously  ascribed  to  the  Excess  in  the 
Length  of  Spring  and  Summer  in  the  Southern  Hemisphere  ;  attributed 
by  Mr.  Lyell  to  the  Operation  of  existing  Causes — Three  Principal  Axes 
of  Rotation — Position  of  the  Axis  of  Rotation  on  the  Surface  of  the  Earth 
invariable — Ocean  not  sufficient  to  restore  the  Equilibrium  of  the  Earth 
if  deranged— Its  Density  and  Mean  Depth— Internal  Structure  of  the 
Earth  m 


CONTENTS.  VJi 

SECTION  XI.  - 

Precession  and  Nutation — Their  Effects  on  the  Apparent  Places  of  the 
Fixed  Stars Page  74 

SECTION  XII. 

Mean  and  Apparent  Sidereal  Time — Mean  and  Apparent  Solar  Time — 
Equation  of  Time — English  and  French  Subdivisions  of  Time — Leap 
Year — Christian  Era — Equinoctial  Time — Remarkable  Eras  depending 
upon  the  Position  of  the  Solar  Perigee — Inequality  of  the  Lengths  of 
the  Seasons  in  the  two  Hemispheres — Application  of  Astronomy  to  Chro- 
nology— English  and  French  Standards  of  Weights  and  Measures  77 

SECTION  XIII. 

Tides — Forces  that  produce  them — Three  kinds  of  Oscillations  in  the  Ocean 
— The  Semidiurnal  Tides — Equinoctial  Tides — Effects  of  the  Declina- 
tion of  the  Sun  and  Moon — Theory  insufficient  without  Observation — 
Direction  of  the  Tidal  Wave— Height  of  Tides— Mass  of  Moon  obtained 
from  her  Action  on  the  Tides — Interference  of  Undulations — Impossi- 
bility of  a  Universal  Inundation — Currents  .  .  .  .  .  85 

SECTION  XIV. 

Repulsive  Force — Interstices  or  Pores — Elasticity — Mossotti's  Theory — 
Gravitation  brought  under  the  same  law  with  Molecular  Attraction  and 
Repulsion — Gases  reduced  to  Liquids  by  Pressure — Intensity  of  the  Co- 
hesive Force — Effects  of  Gravitation — Effects  of  Cohesion — Minuteness 
of  the  ultimate  Atoms  of  Matter — Limited  Height  of  the  Atmosphere — 
Theory  of  Definite  Proportions  and  Relative  Weight  of  Atoms — Dr.  Far- 
aday's Discoveries  with  regard  to  Affinity — Composition  of  Water  by  a 
Plate  of  Platina — Crystalization — Cleavage — Isomorphism — Matter  con- 
sists of  Atoms  of  Definite  Form— Capillary  Attraction  .  96 

SECTION  XV. 

Analysis  of  the  Atmosphere — Its  Pressure — Law  of  Decrease  in  Density — 
Law  of  Decrease  in  Temperature — Measurement  of  Heights  by  the 
Barometer — Extent  of  the  Atmosphere — Barometrical  Variations — Oscil- 
lations— Trade  Winds— Monsoons — Rotation  of  Winds — Laws  of  Hur- 
ricanes— Water-Spouts Ill 

SECTION  XVI. 

Sound — Propagation  of  Sound  illustrated  by  a  Field  of  Standing  Corn — 
Nature  of  Waves — Propagation  of  Sound  through  the  Atmosphere — 
Intensity  —  Noises  —  A  Musical  Sound  —  Quality  —  Pitch  —  Extent  ^of 
Human  Hearing — Velocity  of  Sound  in  Air,  Water,  and  Solids — Causes 
of  the  Obstruction  of  Sound — Law  of  its  Intensity — Reflection  of  Sound 
— Echoes — Thunder — Refraction  of  Sound — Interference  of  Sounds  122 


SECTION  XVII. 

Vibration  of  Musical  Strings — Harmonic  Sounds — Nodes — Vibration  of  Air 
in  Wind  Instruments— Vibration  of  Solids— Vibrating  Plates— Bells- 
Harmony — Sounding-  Boards — Forced  Vibrations—  Resonance — Speaking 
Machines  .  134 


VI11  CONTENTS. 

SECTION  XVIII. 

Refraction — Astronomical  Refraction  and  its  Laws — Formation  of  Tables  of 
Refraction — Terrestrial  Refraction — Its  Quantity — Instances  of  Extraor- 
dinary Refraction — Reflection — Instances  of  Extraordinary  Reflection — 
Loss  of  Light  by  the  Absorbing"  Power  of  the  Atmosphere — Apparent 
Magnitude  of  Sun  and  Moon  in  the  Horizon  .  .  .  Page  147 

SECTION  XIX. 

Constitution  of  Light  according  to  Sir  Isaac  Newton — Absorption  of  Light 
—Colors  of  Bodies— Constitution  of  Light  according  to  Sir  David  Brew- 
ster — New  Colors  in  the  Solar  Spectrum — Fraunhofer's  Dark  Lines — 
Dispersion  of  Light— The  Achromatic  Telescope — Homogeneous  Light — 
Accidental  and  Complementary  Colors — M.  Plateau's  Experiments  and 
Theory  of  Accidental  Colors 153 

SECTION  XX. 

Interference  of  Light — Undulatory  Theory  of  Light — Propagation  of  Light 
— Newton's  Rings — Measurement  of  the  Length  of  the  Waves  of  Light, 
and  of  the  Frequency  of  the  Vibrations  of  Ether  for  each  Color— New- 
ton's Scale  of  Colors — Diffraction  of  Light — Sir  John  HerschePs  Theory 
of  the  Absorption  of  Light — Refraction  and  Reflection  of  Light  161 

SECTION  XXI. 

Polarization  of  Light — Denned — Polarization  by  Refraction — Properties  of 
the  Tourmaline — Double  Refraction — All  doubly  Refracted  Light  is 
Polarized — Properties  of  Iceland  Spar — Tourmaline  absorbs  one  of  the 
two  Refracted  Rays — Undulations  of  Natural  Light — Undulations  ot 
Polarized  Light — The  Optic  Axes  of  Crystals — M.  Fresnel's  Discoveries 
on  the  Rays  passing  along  the  Optic  Axis — Polarization  by  Reflection  172 

SECTION  XXII. 

Phenomena  exhibited  by  the  passage  of  Polarized  Light  through  Mica  and 
Sulphate  of  Lime — The  Colored  Images  produced  by  Polarized  Light 
passing  through  Crystals  having  one  and  two  Optic  Axes — Circular 
Polarization — Elliptical  Polarization — Discoveries  of  MM.  Biot,  Fresnel, 
and  Professor  Airy— Colored  Images  produced  by  the  Interference  of 
Polarized  Rays 180 

SECTION  XXIII. 

Objections  to  the  Undulatory  Theory,  from  a  Difference  in  the  Action  of 
Sound  and  Light  under  the  same  circumstances,  removed — The  Disper- 
sion of  Light  according  to  the  Undulatory  Theory  .  .  .  190 

SECTION  XXIV. 

Chemical  or  Photographic  Rays  of  the  Solar  Spectrum — Messrs.  Scheele, 
Ritter,  a-nd  Wollaston's  Discoveries — Mr.  Wedgewood  and  Sir  Humphry 
Davy's  Photographic  Pictures — The  Calotype — The  Daguerreotype — 
The  Chromatype — The  Cyanotype — Sir  John  Herschel's  Discoveries  in 
the  Photographic  or  Chemical  Spectrum — Mons.  E.  Becquerel's  Discovery 
of  Inactive  Lines  in  the  Chemical  Spectrum  .  .  .  193 


CONTENTS.  ix 

SECTION  XXV. 

Heat — Calorific  Rays  of  the  Solar  Spectrum — Experiments  of  MM.  De 
Laroche  and  Melloui  on  the  Transmission  of  Heat — The  Point  of  greatest 
Heat  in  the  Solar  Spectrum  varies  with  the  Substance  of  the  Prism — 
Polarization  of  Heat— Circular  Polarization  of  Heat — Transmission  of  the 
Chemical  Rays— Absorption  of  Heat— Radiation  of  Heat— Dew— Hoar 
Frost — Rain — Hail — Combustion — Dilatation  of  Bodies  by  Heat — Propa- 
gation of  Heat — Latent  Heat— Heat  presumed  to  consist  of  the  Undula- 
tions of  an  Elastic  Medium — Parathermic  Rays— Moser's  Discoveries 

Page.  906 

SECTION  XXVI. 

Atmosphere  of  the  Planets  and  the  Moon— Constitution  of  the  Sun— Esti- 
mation of  the  Sun's  Light— His  Influence  on  the  different  Planets — 
Temperature  of  Space  —Internal  Heat  of  the  Earth — Zone  of  Constant 
Temperature — Heat  increases  with  the  Depth— Heat  in  Mines  and 
Wells— Thermal  .Springs— Central  Heat— Volcanic  Action— The  Heat 
above  the  Zone  of  Constant  Temperature  entirely  from  the  Sun— The 
Quantity  of  Heat  annually  received  from  the  Sun— Isogeothermal  Lines 
—Distribution  of  Heat  on  the  Earth — Climate — Line  of  Perpetual  Con- 
gelation— Causes  affecting  Climate— Isothermal  Lines — Excessive  Cli- 
mates— The  same  Quantity  of  Heat  annually  received  and  radiated  by 
the  Earth 238 

SECTION  XXVII. 

Influence  of  Temperature  on  Vegetation — Vegetation  varies  with  the  Lati- 
tude and  Height  above  the  Sea— Geographical  Distribution  of  Land 
Plants — Distribution  of  Marine  Plants — Corallines,  Shell-fish,  Reptiles, 
Insects,  Birds,  and  Quadrupeds — Varieties  of  Mankind,  yet  Identity  of 
Species 202 


SECTION  XXVIIL 


Of  ordinary  Electricit 


iry  Electricity,  generally  called  Electricity  of  Tension — Methods 
of  exciting  Bodies — Transference — Electrics  and  Non- Electrics — Law  of 
its  Intensity — Distribution — Tension — Electric  Heat  and  Light — Atmos- 
pheric Electricity— Its  Cause— Electric  Clouds— Back  Stroke— Violent 
Effects  of  Lightning — Its  Velocity— Phosphorescence— Phosphorescent 
Action  of  Solar  Spectrum — Aurora 271 

SECTION  XXIX. 

Voltaic  Electricity — The  Voltaic  Battery — Intensity — Quantity — Compari- 
son of  the  Electricity  of  Tension  with  Electricity  in  Motion— Luminous 
Effects— Decomposition  of  Water— Formation  of  Crystals  by  Voltaic 
Electricity— Electrical  Fish 290 

SECTION  XXX. 

Terrestrial  Magnetism — Magnetic  Poles — Lines  of  equal  and  no  Variation 
'  — The  Dip — The  Magnetic  Equator— Magnetic  Intensity — Secular,  peri- 
odic, and  transitory  Variations  in  the  Magnetic  Phenomena — Origin  of 
the  Mariner's  Compass— Natural  Magnets — Artificial  Magnets — Polarity 
— Induction— Intensity — Hypothesis  of  two  Magnetic  Fluids — Distribu- 
tion of  the  Magnetic  Fluid— Analogy  between  Magnetism  and  Elec- 
tricity    .300 


X  CONTENTS. 

SECTION  XXXI. 

Discovery  of  Electro-Magnetism—Deflection  of  the  Magnetic  Needle  by  a 
Current  of  Electricity — Direction  of  the  Force — Rotatory  Motion  by  Elec- 
tricity— Rotation  of  a  Wire  and  a  Magnet— Rotation  of  a  Magnet  about 
its  Axis — Of  Mercury  and  Water— Electro-Magnetic  Cylinder  or  Helix — 
Suspension  of  a  Needle  in  a  Helix — Electro-Magnetic  Induction — Tem- 
porary Magnets — The  Galvanometer  .  .  .  .  .  Page  314 

SECTION  XXXII. 

Electro-Dynamics—Reciprocal  Action  of  Electric  Currents— Identity  of 
Electro-Dynamic  Cylinders  and  Magnets — Differences  between  the  Ac- 
tion of  Voltaic  Electricity  and  Electricity  of  Tension— Effects  of  a  Voltaic 
Current — Ampere's  Theory .  319 

SECTION  XXXIII. 

Magneto-Electricity— Volta-Electric  Induction— Magneto-Electric  Induc- 
tion— Identity  in  the  Action  of  Electricity  and  Magnetism— Description 
of  a  Magneto-Electric  Apparatus  and  its  Effects — Identity  of  Magnetism 
and  Electricity  .  322 

SECTION  XXXIV. 

Electricity  produced  by  Rotation — Direction  of  the  Currents — Electricity 
from  the  Rotation  of  a  Magnet — M.  Arago's  Experiment  explained — 
Rotation  of  a  Plate  of  Iron  between  the  Poles  of  a  Magnet — Relation  of 
Substances  to  Magnets  of  three  kinds — Thermo-Electricity  .  325 

SECTION  XXXV. 

The  Action  of  Terrestrial  Magnetism  upon  Electric  Currents — Induction 
of  Electric  Currents  by  Terrestrial  Magnetism — The  Earth  Magnetic  by 
Induction — Mr.  Barlow's  Experiment  of  an  Artificial  Sphere— The  Heat 
of  the  Sun  the  Probable  Cause  of  Electric  Currents  in  the  Crust  of  the 
Earth  ;  and  of  the  Variations  in  Terrestrial  Magnetism — Electricity  of 
Metallic  Veins — Terrestrial  Magnetism  possibly  owing  to  Rotation — 
Magnetic  Properties  of  the  Celestial  Bodies— Identity  of  the  Five  Kinds 
of  Electricity — Connection  between  Light,  Heat,  and  Electricity  or  Mag- 
netism  329 

SECTION  XXXVI. 

Ethereal  Medium — Comets — Do  not  disturb  the  Solar  System— Their 
Orbits  and  Disturbances — M.  Faye's  Comet,  probably  the  same-  with 
Lexel's — Periods  of  other  three  known — Halley's — Acceleration  in  the 
Mean  Motions  of  Encke's  and  Biela's  Comets — The  Shock  of  a  Comet — 
Disturbing  Action  of  the  Earth  and  Planets  on  Encke's  and  Biela's 
Comets— Velocity  of  Comets — The  Great  Comet  of  1843 — Physical  Con- 
stitution—Shine by  borrowed  Light — Estimation  of  their  Number  .  337 

SECTION  XXXVII. 

The  Fixed  Stars— Their  Numbers— Estimation  of  their  Distances  and 
Magnitudes  from  their  Light — Stars  that  have  vanished — New  Stars — 
Double  Stars — Binary  and  Multiple  Systems — Their  Orbits  and  Periods 
— Orbitual  and  Parallactic  Motions — Colors — Proper  Motions — General 


CONTENTS.  XI 

Motions  of  all  the  Stars — Clusters — Nebula — Their  Number  and  Forms 
— Double  and  Stellar  Nebulae — Nebulous  Stars — Planetary  Nebulse — 
Constitution  of  the  Nebula?,  and  Forces  which  maintain  them — Distribu- 
tion—Meteorites— Shooting  Stars Page  361 

SECTION  XXXVIII. 

Diffusion  of  Matter  through  Space — Gravitation — Its  Velocity — Simplicity 
of  its  Laws — Gravitation  independent  of  the  Magnitude  and  Distances  of 
the  Bodies — Not  impeded  by  the  Intervention  of  any  Substance — Its 
Intensity  invariable — General  Laws — Recapitulation  and  Conclusion  386 

NOTES       . 391 

INDEX  445 


CONNECTION  OF  PHYSICAL  SCIENCES. 


INTRODUCTION. 

SCIENCE,  regarded  as  the  pursuit  of  truth,  must  ever 
afford  occupation  of  consummate  interest,  and  subject  of 
elevated  meditation.  The  contemplation  of  the  works 
of  creation  elevates  the  mind  to  the  admiration  of  what- 
ever is  great  and  noble  ;  accomplishing  the  object  of  all 
study,  which,  in  the  eloquent  language  of  Sir  James 
Mackintosh,  "is  to  inspire  the  love  of  truth,  of  wisdom, 
of  beauty — especially  of  goodness,  the  highest  beauty 
— and  of  that  supreme  and  eternal  Mind,  which  con- 
tains all  truth  and  wisdom,  all  beauty  and  goodness. 
By  the  love  or  delightful  contemplation  and  pursuit  of 
these  transcendent  aims,  for  their  own  sake  only,  the 
mind  of  man  is  raised  from  low  and  perishable  objects, 
and  prepared  for  those  high  destinies  which  are  ap- 
pointed for  all  those  who  are  capable  of  them." 

Astronomy  affords  the  most  extensive  example  of  the 
connection  of  the  physical  sciences.  In  it  are  combined 
the  sciences  of  number  and  quantity,  of  rest  and  mo- 
tion. In  it  we  perceive  the  operation  of  a  force  which 
is  mixed  up  with  everything  that  exists  in  the  heavens 
or  on  earth;  which  pervades  every  atom,  rules  the 
motions  of  animate  and  inanimate  beings,  and  is  as  sen- 
sible in  the  descent  of  a  rain-drop  as  in  the  falls  of 
Niagara;  in  the  weight  of  the  air,  as  in  the  periods  of 
the  moon.  Gravitation  not  only  binds  satellites  to  their 
planet,  and  planets  to  the  sun,  but  it  connects  sun  with 
sun  throughout  the  wide  extent  of  creation,  and  is  the 
cause  of  the  disturbances,  as  well  as  of  the  order  of 
nature  :  since  every  tremor  it  excites  in  any  one  planet 
is  immediately  transmitted  to  the  farthest  limits  of  the 
system,  in  oscillations,  which  correspond  in  their  periods 
with  the  cause  producing  them,  like  sympathetic  notes 
in  music,  or  vibrations  from  the  deep  tones  of  an  organ. 

The  heavens  afford  the  most  sublime  subject  of  study 
which  can  be  derived  from  science.  The  magnitude 
1  A 


2  INTRODUCTION. 

and  splendor  of  the  objects,  the  inconceivable  rapidity 
with  which  they  move,  and  the  enormous  distances 
between  them,  impress  the  mind  with  some  notion  of 
the  energy  that  maintains  them  in  their  motions,  with  a 
durability  to  which  we  can  see  no  limit.  Equally  con- 
spicuous is  the  goodness  of  the  great  First  Cause,  in 
having  endowed  man  with  faculties,  by  which  he  can 
not  only  appreciate  the  magnificence  of  His  works,  but 
trace,  with  precision,  the  operation  of  His  laws,  use  the 
globe  he  inhabits  as  a  base  wherewith  to  measure  the 
magnitude  and  distance  of  the  sun  and  planets,  and 
make  the  diameter  (Note  1)  of  the  earth's  orbit  the 
first  step  of  a  scale  by  which  he  may  ascend  to  the 
starry  firmament.  Such  pursuits,  while  they  ennoble 
the  mind,  at  the  same  time  inculcate  humility,  by  show- 
ing that  there  is  a  barrier  which  no  energy,  mental  or 
physical,  can  ever  enable  us  to  pass  :  that,  however 
profoundly  we  may  penetrate  the  depths  of  space, 
there  still  remain  innumerable  systems,  compared  with 
which,  those  apparently  so  vast  must  dwindle  into  in- 
significance, or  even  become  invisible  ;  and  that  not  only 
man,  but  the  globe  he  inhabits — nay,  the  whole  system 
of  which  it  forms  so  small  a  part — might  be  annihilated, 
and  its  extinction  be  unperceived  in  the  immensity  of 
creation. 

A  complete  acquaintance  with  physical  astronomy 
can  be  attained  by  those  only  who  are  well  versed  in 
the  higher  branches  of  mathematical  and  mechanical 
science  (N.  2),  and  they  alone  can  appreciate  the  ex- 
treme beauty  of  the  results,  and  of  the  means  by  which 
these  results  are  obtained.  It  is  nevertheless  true,  that 
a  sufficient  skill  in  analysis  (N.  3)  to  follow  the  general 
outline — to  see  the  mutual  dependence  of  the  different 
parts  of  the  system,  and  to  comprehend  by  what  means 
the  most  extraordinary  conclusions  have  been  arrived 
at, — is  within  the  reach  of  many  who  shrink  from  the 
task,  appalled  by  difficulties,  not  more  formidable  than 
those  incident  to  the  study  of  the  elements  of  every 
branch  of  knowledge.  There  is  a  wide  distinction  be- 
tween the  degree  of  mathematical  acquirement  neces- 
sary for  making  discoveries,  and  that  which  is  requisite 
for  understanding  what  others  have  done. 


INTRODUCTION.  3 

Our  knowledge  of  external  objects  is  founded  upon 
experience,  which  furnishes  facts ;  the  comparison  of 
these  facts  establishes  relations,  from  which  the  belief 
that  like  causes  will  produce  like  effects,  leads  to  gen- 
eral laws.  Thus,  experience  teaches  that  bodies  fall  at 
the  surface  of  the  earth  with  an  accelerated  velocity, 
and  with  a  force  proportional  to  their  masses.  By  com- 
parison, Newton  proved  that  the  force  which  occasions 
the  fall  of  bodies  at  the  earth's  surface  is  identical  with 
that  which  retains  the  moon  in  her  orbit;  and  he  con- 
cluded, that  as  the  moon  is  kept  in  her  orbit  by  the 
attraction  of  the  earth,  so  the  planets  might.be  retained 
in  their  orbits  by  the  attraction  of  the  sun.  By  such 
steps  he  was  led  to  the  discovery  of  one  of  those  powers, 
with  which  the  Creator  has  ordained,  that  matter  should 
reciprocally  act  upon  matter. 

Physical  astronomy  is  the  science  which  compares 
and  identifies  the  laws  of  motion  observed  on  earth, 
with  the  motions  that  take  place  in  the  heavens ;  and 
which  traces,  by  an  uninterrupted  chain  of  deduction 
from  the  great  principle  that  governs  the  universe,  the 
revolutions  and  rotations  of  the  planets,  and  the  oscilla- 
tions (N.  4)  of  the  fluids  at  their  surfaces;  and  which 
estimates  the  changes  the  system  has  hitherto  under- 
gone, or  may  hereafter  experience — changes  which 
require  millions  of  years  for  their  accomplishment. 

The  accumulated  efforts  of  astronomers,  from  the 
earliest  dawn  of  civilization,  have  been  necessary  to 
establish  the  mechanical  theoiy  of  astronomy.  The 
courses  of  the  planets  have  been  observed  for  ages,  with 
a  degree  of  perseverance  that  is  astonishing,  if  we  con- 
sider the  imperfection  and  even  the  want  of  instruments. 
The  real  motions  of  the  earth  have  been  separated 
from  the  apparent  motions  of  the  planets ;  the  laws  of 
the  planetary  revolutions  have  been  discovered ;  and 
the  discovery  of  these  laws  has  led  to  the  knowledge  of 
the  gravitation  (N.  5)  of  matter.  On  the  other  hand, 
descending  from  the  principle  of  gravitation,  every  mo- 
tion in  the  solar  system  has  been  so  completely  explained, 
that  the  laws  of  any  astronomical  phenomena  that  may 
hereafter  occur,  are  already  determined. 


ATTRACTION  OP  A  SPHERE.  SKCT.  I. 


SECTION  I. 

Attraction  of  a  Sphere — Form  of  Celestial  Bodies — Terrestrial  Gravitation 
retains  the  Moon  in  her  Orbit — The  Heavenly  Bodies  move  in  Conic 
Sections — Gravitation  proportional  to  Mass — Gravitation  of  the  Particles 
of  Matter — Figure  of  the  Planets — How  it  affects  the  Motions  of  their 
Satellites — Rotation  and  Translation  impressed  by  the  same  Impulse — 
Motion  of  the  Sun  and  Solar  System. 

IT  has  been  proved  by  Newton,  that  a  particle  of  mat- 
ter (N.  G)  placed  without  the  surface  of  a  hollow  sphere 
(N.  7),  is  attracted  by  it  in  the  same  manner  as  if  the 
mass  of  the  hollow  sphere,  or  the  whole  matter  it  con- 
tains, were  collected  into  one  dense  particle  in  its  center. 
The  same  is  therefore  true  of  a  solid  sphere,  which  may 
be  supposed  to  consist  of  an  infinite  number  of  concentric 
hollow  spheres  (N.  8).  This,  however,  is  not  the  case 
with  a  spheroid  (N.  9) ;  but  the  celestial  bodies  are  so 
nearly  spherical,  and  at  such  remote  distances  from  one 
another,  that  they  attract  and  are  attracted  as  if  each 
were  condensed  into  a  single  particle  situate  in  its  center 
of  gravity  (N.  10) — a  circumstance  which  greatly  facili- 
tates the  investigation  of  their  motions. 

Newton  has  shown  that  the  force  which  retains  the 
moon  in  her  orbit,  is  the  same  with  that  which  causes 
heavy  substances  to  fall  at  the  surface  of  the  earth.  If 
the  earth  were  a  sphere,  and  at  rest,  a  body  would  be 
equally  attracted,  that  is,  it  would  have  the  same  weight 
at  every  point  of  its  surface,  because  the  surface  of  a 
sphere  is  everywhere  equally  distant  from  its  center. 
But  as  our  planet  is  flattened  at  the  poles  (N.  11),  and 
bulges  at  the  equator,  the  weight  of  the  same  body 
gradually  decreases  from  the  poles,  where  it  is  greatest, 
to  the  equator,  where  it  is  least.  There  is,  however,  a 
certain  mean  (N.  12)  latitude  (N.  13),  or  pait  of  the  earth 
intermediate  between  the  pole  and  the  equator,  where 
the  attraction  of  the  earth  on  bodies  at  its  surface  is  the 
same  as  if  it  were  a  sphere  ;  and  experience  shows  that 
bodies  there  fall  through  16-0697  feet  in  a  second.  The 
mean  distance  (N.  14)  of  the  moon  from  the  earth  is 
about  sixty  times  the  mean  radius  (N.  15)  of  the  earth. 
When  the  number  16-0697  is  diminished  in  the  ratio 


SECT.  I.  UNIVERSAL  GRAVITATION.  5 

(N.  16)  of  1  to  3600,  which  is  the  square  of  the  moon's 
distance  (N.  17)  from  the  earth's  center,  estimated  in 
terrestrial  radii,  it  is  found  to  be  exactly  the  space  the 
•noon  would  fall  through  in  the  first  second  of  her  de- 
scent to  the  earth,  were  she  not  prevented  by  the  cen- 
trifugal force  (N.  18)  arising  from  the  velocity  with 
which  she  moves  in  her  orbit.  The  moon  is  thus  re- 
tained in  her  orbit  by  a  force  having  the  same  origin, 
and  regulated  by  the  same  law,  with  that  which  causes 
a  stone  to  fall  at  the  earth's  surface.  The  earth  may 
therefore  be  regarded  as  the  center  of  a  force  which 
extends  to  the  moon  ;  and,  as  experience  shows  that  the 
action  and  reaction  of  matter  are  equal  and  contrary 
(N.  19),  the  moon  must  attract  the  earth  with  an  equal 
and  contrary  force. 

Newton  also  ascertained  that  a  body  projected  (N.  20) 
in  space  (N.  21),  will  move  in  a  conic  section  (N.  22),  if 
attracted  by  a  force  proceeding  from  a  fixed  point,  with  an 
intensity  inversely  as  the  square  of  the  distance  (N.  23) ; 
but  that  any  deviation  from  that  Iftw  will  cause  it  to  move 
in  a  curve  of  a  different  nature.  Kepler  found,  by  direct 
observation,  that  the  planets  descripe  ellipses  (N.  24),  or 
oval  paths,  round  the  sun.  Later  observations  show 
that  comets  also  move  in  conic  sections.  It  consequently 
follows,  that  the  sun  attracts  all  the  planets  and  comets 
inversely  as  the  square  of  their  distance?  from  his  cen- 
ter ;  the  sun,  therefore,  is  the  center  of  a  force  extend- 
ing indefinitely  in  space,  and  including  all  the  bodies  of 
the  system  in  its  action. 

Kepler  also  deduced  from  observation,  that  the  squares 
of  the  periodic  times  (N.  25)  of  the  planets,  or  the  times 
of  their  revolutions  round  the  sun,  are  proportional  to 
the  cubes  of  their  mean  distances  from  his  center 
(N.  26).  Hence  the  intensity  of  gravitation  of  all  the 
bodies  toward  the  sun  is  the  same  at  equal  distances. 
Consequently,  gravitation  is  proportional  to  the  masses 
(N.  27);  for,  if  the  planets  and  comets  were  at  equal 
distances  from  the  sun,  and  left  to  the  effects  of  gravity, 
they  would  arrive  at  his  surface  at  the  same  time 
(N.  28).  The  satellites  also  gravitate  to  their  primaries 
(N.  29)  according  to  the  same  law  that  their  primaries 
do  to  the  sun.  Thus,  by  the  law  of  action  and  reaction, 
Afl 


6  FORM  OF  PLANETS.  SBCT.  I. 

each  body  is  itself  the  center  of  an  attractive  force  ex- 
tending indefinitely  in  space,  causing  all  the  mutual  dis- 
turbances which  render  the  celestial  motions  so  compli- 
cated, and  their  investigation  so  difficult. 

The  gravitation  of  matter  directed  to  a  center,  and 
attracting  directly  as  the  mass,  and  inversely  as  the 
square  of  the  distance,  does  not  belong  to  it  when  con- 
sidered in  mass  only ;  particle  acts  on  particle  according 
to  the  same  law  when  at  sensible  distances  from  each 
other.  If  the  sun  acted  on  the  center  of  the  earth,  with- 
out attracting  each  of  its  particles,  the  tides  would  be 
very  much  greater  than  they  now  are,  and  would  also, 
in  other  respects,  be  very  different.  The  gravitation  of 
the  earth  to  the  sun  results  from  the  gravitation  of  all  its 
particles,  which,  in  their  turn,  attract  the  sun  in  the  ra- 
tio of  their  respective  masses.  There  is  a  reciprocal 
action,  likewise,  between  the  earth  and  every  particle 
at  its  surface.  The  earth  and  a  feather  mutually  attract 
each  other  in  the  proportion  of  the  mass  of  the  earth  to 
the  mass  of  the  feather.  Were  this  not  the  case,  and 
were  any  portion  of  the  earth,  however  small,  to  attract 
another  portion,  and  not  be  itself  attracted,  the  center  of 
gravity  of  the  earth  would  be  moved  in  space  by  this 
action,  which  is  impossible. 

The  forms  of  the  planets  result  from  the  reciprocal 
attraction  of  their  component  particles.  A  detached  fluid 
mass,  if  at  rest,  would  assume  the  form  of  a  sphere, 
from  the  reciprocal  attraction  of  its  particles.  But  if  the 
mass  revolve  about  an  axis,  it  becomes  flattened  at  the 
poles,  and  bulges  at  the  equator  (N.  11),  in  consequence 
of  the  centrifugal  force  arising  from  the  velocity  of  rota- 
tion (N.  30) ;  for  the  centrifugal  force  diminishes  the 
gravity  of  the  particles  at  the  equator,  and  equilibrium 
can  only  exist  where  these  two  forces  are  balanced  by 
an  increase  of  gravity.  Therefore,  as  the  attractive  force 
is  the  same  on  all  particles  at  equal  distances  from  the 
center  of  a  sphere,  the  equatorial  particles  would  recede 
from  the  center,  till  their  increase  in  number  balance 
the  centrifugal  force  by  their  attraction.  Consequently, 
the  sphere  would  become  an  oblate,  or  flattened  sphe- 
roid ;  and  a  fluid  partially  or  entirely  covering  a  solid,  as 
the  ocean  and  atmosphere  cover  the  earth,  must  assume 


SECT.  I.  ROTATION  AND  TRANSLATION.  7 

that  form  in  order  to  remain  in  equilibrio.  The  surface 
of  the  sea  is  therefore  spheroidal,  and  the  surface  of  the 
earth  only  deviates  from  that  figure  where  it  rises  above 
or  sinks  below  the  level  of  the  sea.  But  the  deviation  is 
so  small,  that  it  is  unimportant  when  compared  with  the 
magnitude  of  the  earth ;  for  the  mighty  chain  of  the 
Andes,  and  the  yet  more  lofty  Himalaya,  bear  about  the 
same  proportion  to  the  earth  that  a  grain  of  sand  does  to 
a  globe  three  feet  in  diameter.  Such  is  the  form  of  the 
earth  and  planets.  The  compression  (N.  31)  or  flatten- 
ing at  their  poles  is,  however,  so  small,  that  even  Jupiter, 
whose  rotation  is  the  most  rapid,  and  therefore  the  most 
elliptical  of  the  planets,  may,  from  his  great  distance,  be 
regarded  as  spherical.  Although  the  planets  attract 
each  other  as  if  they  were  spheres,  on  account  of  their 
distances,  yet  the  satellites  (N.  32)  are  near  enough  to 
be  sensibly  affected  in  their  motions  by  the  forms  of 
their  primaries.  The  moon,  for  example,  is  so  near 
the  earth,  that  the  reciprocal  attraction  between  each  of 
her  particles,  and  each  of  the  particles  in  the  prominent 
mass  at  the  terrestrial  equator,  occasions  considerable 
disturbances  in  the  motions  of  both  bodies ;  for  the  ac- 
tion of  the  moon  on  the  matter  at  the  earth's  equator, 
produces  a  nutation  (N.  33)  in  the  axis  (N.  34)  of  rotation, 
and  the  reaction  of  that  matter  on  the  moon  is  the  cause 
of  a  corresponding  nutation  in  the  lunar  orbit  (N.  35). 

If  a  sphere  at  rest  in  space  receive  an  impulse  passing 
through  its  center  of  gravity,  all  its  parts  will  move  with 
an  equal  velocity  in  a  straight  line  ;  but  if  the  impulse 
does  not  pass  though  the  center  of  gravity,  its  particles, 
having  unequal  velocities,  will  have  a  rotatory  or  revolv- 
ing motion,  at  the  same  time  that  it  is  translated  (N.  36) 
in  space.  These  motions  are  independent  of  one  an- 
other ;  so  that  a  contrary  impulse,  passing  through  its 
center  of  gravity,  will  impede  its  progress,  without  in- 
terfering with  its  rotation.  As  the  sun  rotates  about  an 
axis,  it  seems  probable,  if  an  impulse  in  a  contrary  direc- 
tion has  not  been  given  to  his  center  of  gravity,  that  he 
moves  in  space,  accompanied  by  all  those  bodies  which 
compose  the  solar  system — a  circumstance  which  would 
in  no  way  interfere  with  their  relative  motions ;  for,  in 
consequence  of  the  principle,  that  force  is  proportional 


8  ELLIPTICAL  MOTION.  SECT.  II. 

to  velocity  (N.  37),  the  reciprocal  Attractions  of  a  system 
remain  the  same,  whether  its  center  of  gravity  be  at 
rest,  or  moving  uniformly  in  space.  It  is  computed  that, 
had  the  earth  received  its  motion  from  a  single  impulse, 
that  impulse  must  have  passed  through  a  point  about 
twenty-five  miles  from  its  center. 

Since  the  motions  of  rotation  and  translation  of  the 
planets  are  independent  of  each  other,  though  probably 
communicated  by  the  same  impulse,  they  form  separate 
subjects  of  investigation. 


SECTION  II. 

Elliptical  Motion — Mean  and  True  Motion — Equinoctial — Ecliptic — Equi- 
noxes— Mean  and  True  Longitude — Equation  of  Center — Inclination  of 
the  Orbits  of  Planets — Celestial  Latitude — Nodes — Elements  of  an  Orbit 
— Undisturbed  or  Elliptical  Orbits — Great  Inclination  of  the  Orbits  of 
the  new  Planets — Universal  Gravitation  the  Cause  of  Perturbations  in 
the  Motions  of  the  Heavenly  Bodies — Problem  of  the  Three  Bodies — 
Stability  of  Solar  System  depends  upon  the  Primitive  Momentum  of  the 
Bodies. 

A  PLANET  moves  in  its  elliptical  orbit  with  a  velocity 
varying  every  instant,  in  consequence  of  two  forces,  one 
tending  to  the  center  of  the  sun,  and  the  other  in  the 
direction  of  a  tangent  (N.  38)  to  its  orbit,  arising  from 
the  primitive  impulse,  given  at  the  time  when  it  was 
launched  into  space.  Should  the  force  in  the  tangent 
cease,  the  planet  would  fall  to  the  sun  by  its  gravity. 
Were  the  sun  not  to  attract  it,  the  planet  would  fly  off 
in  the  tangent.  Thus,  when  the  planet  is  at  the  point 
of  its  orbit  farthest  from  the  sun,  his  action  overcomes 
the  planet's  velocity,  and  brings  it  toward  him  with 
such  an  accelerated  motion,  that  at  last  it  overcomes  the 
sun's  attraction  ;  and  shooting  past  him,  gradually  de- 
creases in  velocity,  until  it  arrives  at  the  most  distant 
point,  where  the  sun's  attraction  again  prevails  (N.  39). 
In  this  motion  the  radii  vector es  (N.  40),  or  imaginary 
lines  joining  the  centers  of  the  sun  and  the  planets,  pass 
over  equal  areas  or  spaces  in  equal  times  (N.  41). 

The  mean  distance  of  a  planet  from  the  sun  is  equal 
to  half  the  major  axis  (N.  42)  of  its  orbit :  if,  therefore, 
the  planet  described  a  circle  (N.  43)  round  the  sun  at 


S«CT.  IL  ELLIPTICAL  MOTION.  9 

its  mean  distance,  the  motion  would  be  uniform,  and 
the  periodic  time  unaltered,  because  the  planet  would 
arrive  at  the  extremities  of  the  major  axis  at  the  same 
instant,  and  would  have  the  same  velocity,  whether  it 
moved  in  the  circular  or  elliptical  orbit,  since  the  curves 
coincide  in  these  points.  But,  in  every  other  part,  the 
elliptical  or  true  motion  (N.  44)  would  either  be  faster 
or  slower  than  the  circular  or  mean  motion  (N.  45).  As 
it  is  necessary  to  have  some  fixed  point  in  the  heavens 
from  whence  to  estimate  these  motions,  the  vernal  equi- 
nox (N.  46)  at  a  given  epoch  has  been  chosen.  The 
equinoctial,  which  is  a  great  circle  traced  in  the  starry 
heavens  by  the  imaginary  extension  of  the  plane  of  the 
terrestrial  equator,  is  intersected  by  the  ecliptic,  or  ap- 
parent path  of  the  sun,  in  two.  points  diametrically  oppo- 
site to  one  another,  called  the  vernal  and  autumnal 
equinoxes.  The  vernal  equinox  is  the  point  through 
which  the  sun  passes,  in  going  from  the  southern  to  the 
northern  hemisphere ;  and  the  autumnal,  that  in  which 
he  crosses  from  the  northern  to  the  southern.  The 
mean  or  circular  motion  of  a  body,  estimated  from  the 
vernal  equinox,  is  its  mean  longitude ;  and  its  elliptical, 
or  true  motion,  reckoned  from  that  point,  is  its  true  lon- 
gitude (N.  47) :  both  being  estimated  from  west  to  east, 
the  direction  in  which  the  bodies  move.  The  difference 
between  the  two  is  called  the  equation  of  the  center 
(N.  48) ;  which  consequently  vanishes  at  the  apsides 
(N.  49),  or  extremities  of  the  major  axis,  and  is  at  its 
maximum  ninety  degrees  (N.  50)  distant  from  these 
points,  or  in  quadratures  (N.  51),  where  it  measures 
the  eccentricity  (N.  52)  of  the  orbit ;  so  that  the  place 
of  a  planet  in  its  elliptical  orbit  is  obtained,  by  adding  or 
subtracting  the  equation  of  the  center  to  or  from  its 
mean  longitude. 

The  orbits  of  the  planets  have  a  very  small  obliquity 
or  inclination  (N.  53)  to  the  plane  of  the  ecliptic  in  which 
the  earth  moves ;  and  on  that  account,  astronomers  refer 
their  motions  to  this  plane  at  a  given  epoch  as  a  known 
and  fixed  position.  The  angular  distance  of  a  planet 
from  the  plane  of  the  ecliptic  is  its  latitude  (N.  54) ; 
which  is  south  or  north,  according  as  the  planet  is  south 
or  north  of  that  plane.  When  the  planet  10  in  the  plane 


10  ORBITS  OF  THE  PLANETS.  SECT.  II. 

of  the  ecliptic,  its  latitude  is  zero  :  it  is  then  said  to  be 
in  its  nodes  (N.  55).  The  ascending  node  is  that  point 
in  the  ecliptic,  through  which  the  planet  passes,  in  going 
from  the  southern  to  the  northern  hemisphere.  The 
descending  node  is  a  corresponding  point  in  the  plane  of 
the  ecliptic  diametrically  opposite  to  the  other,  through 
which  the  planet  descends  in  going  from  the  northern 
to  the  southern  hemisphere.  The  longitude  and  lati- 
tude of  a  planet  cannot  be  obtained  by  direct  observa- 
tion, but  are  deduced  from  observations  made  at  the 
surface  of  the  earth,  by  a  very  simple  computation. 
These  two  quantities,  however,  will  not  give  the  place 
of  a  planet  in  space.  Its  distance  from  the  sun  (N.  56) 
must  also  be  known ;  and,  for  the  complete  determina- 
tion of  its  elliptical  motion,  the  nature  and  position  of  its 
orbit  must  be  ascertained  by  observation.  This  depends 
upon  seven  quantities,  called  the  elements  of  the  ortyt 
(N.  57).  These  are,  the  length  of  the  major  axis,  and 
the  eccentricity,  which  determine  the  form  of  the  orbit: 
the  longitude  of  the  planet  when  at  its  least  distance 
from  the  sun,  called  the  longitude  of  the  perihelion  ;  the 
inclination  of  the  orbit  to  the  plane  of  the  ecliptic,  and 
the  longitude  of  its  ascending  node ;  these  give  the  po- 
sition of  the  orbit  in  space  ;  but  the  periodic  time,  and 
the  longitude  of  the  planet  at  a  given  instant,  called  the 
longitude  of  the  epoch,  are  necessary  for  finding  the 
place  of  the  body  in  its  orbit  at  all  times.  A  perfect 
knowledge  of  these  seven  elements  is  requisite,  for  as- 
certaining all  the  circumstances  of  undisturbed  elliptical 
motion.  By  such  means  it  is  found,  that  the  paths  of 
the  planets,  when  their  mutual  disturbances  are  omitted, 
are  ellipses  nearly  approaching  to  circles,  whose  planes, 
slightly  inclined  to  the  ecliptic,  cut  it  in  straight  lines, 
passing  through  the  center  of  the  sun  (N.  58).  The 
orbits  of  the  recently  discovered  planets  deviate  more 
from  the  ecliptic  than  those  of  the  ancient  planets ;  that 
of  Pallas,  for  instance,  has  an  inclination  of  34°  37'  50-2" 
to  it ;  on  which  account  it  is  more  difficult  to  determine 
their  motions. 

Were  the  planets  attracted  by  the  sun  only,  they 
would  always  move  in  ellipses,  invariable  in  form  and 
position ;  and  because  his  action  is  proportional  to  his 


S*CT.  II.          PROBLEM  OF  THE  THREE  BODIES.  11 

mass,  which  is  much  larger  than  that  of  all  the  planets 
put  together,  the  elliptical  is  the  nearest  approximation 
to  their  true  motions.  The  true  motions  of  the  planets 
are  extremely  complicated,  in  consequence  of  their 
mutual  attraction;  so  that  they  do  not  move  in  any 
known  or  symmetrical  curve,  but  in  paths  now  ap- 
proaching to,  now  receding  from,  the  elliptical  form ; 
and  their  radii  vectores  do  not  describe  areas  or  spaces 
exactly  proportional  to  the  time,  so  that  the  areas  be- 
come a  test  of  disturbing  forces. 

To  determine  the  motion  of  each  body,  when  dis- 
turbed by  all  the  rest,  is  beyond  the  power  of  analysis. 
It  is  therefore  necessary  to  estimate  the  disturbing  ac- 
tion of  one  planet  at  a  time,  whence  the  celebrated 
problem  of  the  three  bodies,  originally  applied  to  the 
moon,  the  earth,  and  the  sun ;  namely,  the  masses 
being  given  of  three  bodies  projected  from  three  given 
points,  with  velocities  given  both  in  quantity  and  direc- 
tion ;  and,  supposing  the  bodies  to  gravitate  to  one  an- 
other with  forces  that  are  directly  as  their  masses,  and 
Diversely  as  the  squares  of  the  distances,  to  find  the 
lines  described  by  these  bodies,  and  their  positions  at 
any  given  instant :  or,  in  other  words,  to  determine  the 
path  of  a  celestial  body  when  attracted  by  a  second  body, 
and  disturbed  in  its  motion  round  the  second  body  by  a 
third — a  problem  equally  applicable  to  planets,  satellites, 
and  comets. 

By  this  problem  the  motions  of  translation  of  the 
celestial  bodies  are  determined.  It  is  an  extremely 
difficult  one,  and  would  be  infinitely  more  so,  if  the  dis- 
turbing action  were  not  very  small  when  compared  with 
the  central  force  ;  that  is,  if  the  action  of  the  planets  on 
one  another  were  not  veiy  small  when  compared  with 
that  of  the  sun.  As  the  disturbing  influence  of  each 
body  may  be  found  separately,  it  is  assumed  that  the 
action  of  the  whole  system,  in  disturbing  any  one  planet, 
is  equal  to  the  sum  of  all  the  particular  disturbances  it 
experiences,  on  the  general  mechanical  principle,  that 
the  sum  of  any  number  of  small  oscillations  is  nearly 
equal  to  their  simultaneous  and  joint  effect. 

On  account  of  the  reciprocal  action  of  matter,  the 
stability  of  the  system  depends  upon  the  intensity  of  the 


12  STABILITY  OF  SYSTEM.  SECT.  III. 

primitive  momentum  (N.  59)  of  the  planets,  and  the 
ratio  of  their  masses  to  that  of  the  sun ;  for  the  nature 
of  the  conic  sections  in  which  the  celestial  bodies  move, 
depends  upon  the  velocity  with  which  they  were  first 
propelled  in  space.  Had  that  velocity  been  such  as  to 
make  the  planets  move  in  orbits  of  unstable  equilibrium 
(N.  60),  their  mutual  attractions  might  have  changed 
them  into  parabolas,  or  even  hyperbolas  (N.  22) ;  so 
that  the  earth  and  planets  might,  ages  ago,  have  been 
sweeping  far  from  our  sun  through  the  abyss  of  space. 
But  as  the  orbits  differ  very  little  from  circles,  the  mo- 
mentum of  the  planet,  when  projected,  must  have  been 
exactly  sufficient  to  insure  the  permanency  and  stability 
of  the  system.  Besides,  the  mass  of  the  sun  is  vastly 
greater  than  that  of  any  planet ;  and  as  their  inequali- 
ties bear  the  same  ratio  to  their  elliptical  motions,  that 
their  masses  do  to  that  of  the  sun,  their  mutual-  disturb- 
ances only  increase  or  diminish  the  eccentricities  of  their 
orbits,  by  very  minute  quantities  ;  consequently  the  mag- 
nitude of  the  sun's  mass  is  the  principal  cause  of  the 
stability  of  the  system.  There  is  not  in  the  physical 
world  a  more  splendid  example  of  the  adaptation  of 
means  to  the  accomplishment  of  an  end,  than  is  exhib- 
ited in  the  nice  adjustment  of  these  forces,  at  once  the 
cause  of  the  variety  and  of  the  order  of  Nature. 


SECTION  III. 

Perturbations,  Periodic  and  Circular — Disturbing  Action  equivalent  to 
three  Partial  Forces — Tangential  Force  the  Cause  of  the  Periodic  Ine 
qualities  in  Longitude,  and  Secular  Inequalities  in  the  Form  and  Position 
of  the  Orbit  in  its  own  Plane — Radial  Force  the  Cause  of  Variations  in 
the  Planet's  Distance  from  the  Sun — It  combines  with  the  Tangential 
Force  to  produce  the  Secular  Variations  in  the  Form  and  Position  of  the 
Orbit  in  its  own  Plane — Perpendicular  Force  the  Cause  of  Periodic  Per- 
turbations in  Latitude,  and  Secular  Variations  in  the  Position  of  the 
Orbit  with  regard  to  the  Plane  of  the  Ecliptic — Mean  Motion  and  Major 
Axis  Invariable — Stability  of  System — Effects  of  a  Resisting  Medium — 
Invariable  Plane  of  the  Solar  System  and  of  the  Universe — Great  Ine- 
quality of  Jupiter  and  Saturn. 

THE  planets  are  subject  to  disturbances  of  two  kinds, 
both  resulting  from  the  constant  operation  of  their  recip- 
rocal attraction :  one  kind,  depending  upon  their  posi- 


SECT.  III.  PERTURBATIONS.  13 

tions  with  regard  to  each  other,  begins  from  zero,  in- 
creases to  a  maximum,  decreases,  and  becomes  zero 
again,  when  the  planets  return  to  the  same  relative 
positions.  In  consequence  of  these,  the  disturbed  planet 
is  sometimes  drawn  away  from  the  sun,  sometimes 
brought  nearer  to  him  :  sometimes  it  is  accelerated  in 
its  motion,  and  sometimes  retarded.  At  one  time  it  is 
drawn  above  the  plane  of  its  orbit,  at  another  time  below 
it,  according  to  the  position  of  the  disturbing  body.  All 
such  changes,  being  accomplished  in  short  periods,  some 
in  a  few  months,  others  in  years,  or  in  hundreds  of 
years,  are  denominated  periodic  inequalities.  The  in- 
equalities of  the  other  kind,  though  occasioned  likewise 
by  the  disturbing  energy  of  the  planets,  are  entirely  in- 
dependent of  their  relative  positions.  They  depend 
upon  the  relative  positions  of  the  orbits  alone,  whose 
forms  and  places  in  space  are  altered  by  very  minute 
quantities,  in  immense  periods  of  time,  and  are,  there- 
fore, called  secular  inequalities. 

The  periodical  perturbations  are  compensated,  when 
the  bodies  return  to  the  same  relative  positions  with 
regard  to  one  another  and  to  the  sun :  the  secular  ine- 
qualities are  compensated,  when  the  orbits  return  to 
the  same  positions  relatively  to  one  another,  and  to  the 
plane  of  the  ecliptic. 

Planetary  motion,  including  both  these  kinds  of  dis- 
turbance, may  be  represented  by  a  body  revolving  in  an 
ellipse,  and  making  small  and  transient  deviations,  now 
on  one  side  of  its  path,  and  now  on  the  other,  while  the 
ellipse  itself  is  slowly,  but  perpetually,  changing  both  in 
form  and  position. 

The  periodic  inequalities  are  merely  transient  devi- 
ations of  a  planet  from  its  path,  the  most  remarkable  of 
which  only  lasts  about  918  years;  but,  in  consequence 
of  the  secular  disturbances,  the  apsides,  or  extremities 
of  the  major  axes  of  all  the  orbits,  have  a  direct  but 
variable  motion  in  space,  excepting  those  of  the  orbit  of 
Venus,  which  are  retrograde  (N.  61),  and  the  lines  of 
the  nodes  move  with  a  variable  velocity  in  a  contrary 
direction.  Besides  these,  the  inclination  and  eccen- 
tricity of  every  orbit  are  in  a  state  of  perpetual-  but  slow 
change.  These  effects  result  from  the  disturbing  action 
B 


14  D1STUKBING  FORCES.  SJBCT.  III. 

of  all  the  planets  on  each.  But  as  it  is  only  necessary 
to  estimate  the  disturbing  influence  of  one  body  at  a 
time,  what  follows  may  convey  some  idea  of  the  manner 
in  which  one  planet  disturbs  the  elliptical  motion  of 
another. 

Suppose  two  planets  moving  in  ellipses  round  the  sun  ; 
if  one  of  them  attracted  the  other  and  the  sun  with 
equal  intensity,  and  in  parallel  directions  (N.  62),  it 
would  have  no  effect  in  disturbing  the  elliptical  motion. 
The  inequality  of  this  attraction  is  the  sole  cause  of 
perturbation,  and  the  difference  between  the  disturbing 
planet's  action  on  the  sun  and  on  the  disturbed  planet 
constitutes  the  disturbing  force,  which  consequently 
varies  in  intensity  and  direction  with  every  change  in 
the  relative  positions  of  the  three  bodies.  Although 
both  the  sun  and  planet  are  under  the  influence  of  the 
disturbing  force,  the  motion  of  the  disturbed  planet  is 
referred  to  the  center  of  the  sun  as  a  fixed  point,  for 
convenience.  The  whole  force  (N.  63)  which  disturbs 
a  planet  is  equivalent  to  three  partial  forces.  One  of 
these  acts  on  the  disturbed  planet,  in  the  direction  of  a 
tangent  to  its  orbit,  and  is  called  the  tangential  force  :  it 
occasions  secular  inequalities  in  the  form  and  position  of 
the  orbit  in  its  own  plane,  and  is  the  sole  cause  of  the 
periodical  perturbations  in  the  planet's  longitude.  An- 
other acts  upon  the  same  body  in  the  direction  of  its 
radius  vector,  that  is,  in  the  line  joining  the  centers  of 
the  sun  and  planet,  and  is  called  the  radial  force  :  it 
produces  periodical  changes  in  the  distance  of  the  planet 
from  the  sun,  and  affects  the  form  and  position  of  the 
orbit  in  its  own  plane.  The  third,  which  may  be  called 
the  perpendicular  force,  acts  at  right  angles  to  the  plane 
of  the  orbit,  occasions  the  periodic  inequalities  in  the 
planet's  latitude,  and  affects  the  position  of  the  orbit 
with  regard  to  the  plane  of  the  ecliptic. 

It  has  been  observed,  that  the  radius  vector  of  a 
planet  moving  in  a  perfectly  elliptical  orbit,  passes  over 
equal  spaces  or  areas  in  equal  times;  a  circumstance 
which  is  independent  of  the  law  of  the  force,  and  would 
be  the  same  whether  it  varied  /inversely  as  the  square 
of  the  distance,  or  not,  provided  only  that  it  be  directed 
to  the  center  of  the  sun.  Hence  the  tangential  force. 


SICT.  III.  MOTION  OF  THE  APSIDES.  15 

not  being  directed  to  the  center,  occasioas  an  unequable 
description  of  areas,  or,  what  is  the  same  thing,  it  dis- 
turbs the  motion  of  the  planet  in  longitude.  The  tan- 
gential force  sometimes  accelerates  the  planet's  motion, 
sometimes  retards  it,  and  occasionally  has  no  effect  at  all. 
Were  the  orbits  of  both  planets  circular,  a  complete 
compensation  would  take  place  at  each  revolution  of  the 
two  planets,  because  the  arcs  in  which  the  accelerations 
and  retardations  take  place,  would  be  symmetrical  on 
each  side  of  the  disturbing  force.  For  it  is  clear,  that 
if  the  motion  be  accelerated  through  a  certain  space,  and 
then  retarded  through  as  much,  the  motion  at  the  end 
of  the  time  will  be  the  same  as  if  no  change  had  taken 
place.  But,  as  the  orbits  of  the  planets  are  ellipses,  this 
symmetry  does  not  hold  ;  for,  as  the  planet  moves  un- 
equably  in  its  orbit,  it  is  in  some  positions  more  directly, 
and  for  a  longer  time,  under  the  influence  of  the  dis- 
turbing force  than  in  others.  And  although  multitudes 
of  variations  do  compensate  each  other  in  short  periods, 
there  are  others,  depending  on  peculiar  relations  among 
the  periodic  times  of- the  planets,  which  do  not  compen- 
sate each  other  till  after  one,  or  even  till  after  many 
revolutions  of  both  bodies.  A  periodical  inequality  of 
this  kind  in  the  motions  of  Jupiter  and  Saturn,  has  a 
period  of  no  less  than  918  years. 

The  radial  force,  or  that  part  of  the  disturbing  force 
which  acts  in  the  direction  of  the  line  joining  the  centers 
of  the  sun  and  disturbed  planet,  has  no  effect  on  the 
areas,  but  is  the  cause  of  periodical  changes  of  small 
extent  in  the  distance  of  the  planet  from  the  sun.  It 
has  already  been  shown,  that  the  force  producing  per- 
fectly elliptical  motion  varies  inversely  as  the  square  of 
the  distance,  and  that  a  force  following  any  other  law 
would  cause  the  body  to  move  in  a  curve  of  a  very  dif- 
ferent kind.  Now,  the  radial  disturbing  force  varies 
directly  as  the  distance ;  and,  as  it  sometimes  combines 
with  and  increases  the  intensity  of  the  sun's  attraction 
for  the  disturbed  body,  and  at  other  times  opposes  and 
consequently  diminishes  it,  in  both  cases  it  causes  the 
sun's  attraction  to  deviate  from  the  exact  law  of  gravity, 
and  the  whole  action  of  this  compound  central  force  on 
the  disturbed  body  is  either  greater  or  less  than  what  is 


16  MOTION  OF  THE  APSIDES.  SKCT.  111. 

requisite  for  perfectly  elliptical  motion.  When  greater, 
the  curvature  of  the  disturbed  planet's  path  on  leaving 
its  perihelion  (N.  64),  or  point  nearest  the  sun,  is 
greater  than  it  would  be  in  the  ellipse,  which  brings  the 
planet  to  its  aphelion  (N.  65),  or  point  farthest  from  the 
sun,  before  it  has  passed  through  180°,  as  it  would  do 
if  undisturbed.  So  that  in  this  case  the  apsides,  or  ex- 
tremities of  the  major  axis,  advance  in  space.  When 
the  central  force  is  less  than  the  law  of  gravity  requires, 
the  curvature  of  the  planet's  path  is  less  than  the  cur- 
vature of  the  ellipse.  So  that  the  planet,  on  leaving  its 
perihelion,  would  pass  through  more  than  180°  before 
arriving  at  its  aphelion,  which  causes  the  apsides  to  re- 
cede in  space  (N.  66).  Cases  both  of  advance  and  re- 
cess occur  during  a  revolution  of  the  two  planets ;  but 
those  in  which  the  apsides  advance,  preponderate. 
This,  however,  is  not  the  full  amount  of  the  motion  of 
the  apsides  ;  part  arises  also  from  the  tangential  force 
(N.  63),  which  alternately  accelerates  and  retards  the 
velocity  of  the  disturbed  planet.  An  increase  in  the 
planet's  tangential  velocity  diminishes  the  curvature  of 
its  orbit,  and  is  equivalent  to  a  decrease  of  central  force. 
On  the  contrary,  a  decrease  of  the  tangential  velocity, 
which  increases  the  curvature  of  the  orbit,  is  equivalent 
to  an  increase  of  central  force.  These  fluctuations, 
owing  to  the  tangential  force,  occasion  an  alternate  re- 
cess and  advance  of  the  apsides,  after  the  manner 
already  explained  (N.  66).  An  uncompensated  portion 
of  the  direct  motion  arising  from  this  cause,  conspires 
with  that  already  impressed  by  the  radial  force,  and  in 
some  cases  even  nearly  doubles  the  direct  motion  of 
these  points.  The  motion  of  the  apsides  may  be  repre- 
sented, by  supposing  a  planet  to  move  in  an  ellipse, 
while  the  ellipse  itself  is  slowly  revolving  about  the  sun 
in  the  same  plane  (N.  67).  This  motion  of  the  major 
axis,  which  is  direct  in  all  the  orbits  except  that  of  the 
planet  Venus,  is  irregular,  and  so  slow,  that  it  requires 
more  than  109,830  years  for  the  major  axis  of  the 
earth's  orbit  to  accomplish  a  sidereal  revolution  (N.  68), 
that  is,  to  return  to  the  same  stars;  and  20,984  years 
to  complete  its  tropical  revolution  (N.  69),  or  to  return 
to  the  same  equinox.  The  difference  between  these 


SBCT.  III.        VARIATION  LN  THE  ECCENTRICITY.  17 

two  periods  arises  from  a  retrograde  motion  in  the 
equinoctial  point,  which  meets  the  advancing  axis  be- 
fore it  has  completed  its  revolution  with  regard  to  the 
stars.  The  major  axis  of  Jupiter's  orbit  requires  no 
less  than  200,610  years  to  perform  its  sidereal  revolution, 
and  22,743  years  to  accomplish  its  tropical  revolution 
from  the  disturbing  action  of  Saturn  alone. 

A  variation  in  the  eccentricity  of  the  disturbed  planet's 
orbit,  is  an  immediate  consequence  of  the  deviation  from 
elliptical  curvature,  caused  by  the  action  of  the  dis- 
turbing force.  When  the  path  of  the  body,  in  pro- 
ceeding from  its  perihelion  to  its  aphelion,  is  more  curved 
than  it  ought  to  be  from  the  effect  of  the  disturbing  forces, 
it  falls  within  the  elliptical  orbit,  the  eccentricity  is  di- 
minished, and  the  orbit  becomes  more  nearly  circular ; 
when  that  curvature  is  less  than  it  ought  to  be,  the  path 
of  the  planet  falls  without  its  elliptical  orbit  (N.  66),  and 
the  eccentricity  is  increased  :  during  these  changes,  the 
length  of  the  major  axis  is  not  altered,  the  orbit  only 
bulges  out,  or  becomes  more  flat  (N.  70).  Thus  the 
variation  in  the  eccentricity  arises  from  the  same  cause 
that  occasions  the  motion  of  the  apsides  (N.  67).  There 
is  an  inseparable  connection  between  these  two  ele- 
ments ;  they  vary  simultaneously,  and  have  the  same 
period ;  so  that  while  the  major  axis  revolves  in  an  im- 
mense period  of  time,  the  eccentricity  increases  and 
decreases  by  very  small  quantities,  and  at  length  returns 
to  its  original  magnitude  at  each  revolution  of  the  ap- 
sides. The  terrestrial  eccentricity  is  decreasing  at  the 
rate  of  about  40  miles  annually ;  and,  if  it  were  to  de- 
crease equably,  it  would  be  39,861  years  before  the 
earth's  orbit  became  a  circle.  The  mutual  action  of 
Jupiter  and  Saturn  occasions  variations  in  the  eccentri- 
city of  both  orbits,  the  greatest  eccentricity  of  Jupiter's 
orbit  corresponding  to  the  least  of  Saturn's.  The 
period  in  which  these  vicissitudes  are  accomplished  is 
70,414  years,  estimating  the  action  of  these  two  planets 
alone  :  but  if  the  action  of  all  the  planets  were  estimated, 
the  cycle  would  extend  to  millions  of  years. 

That  part  of  the  disturbing  force  is  now  to  be  con- 
sidered which  acts  perpendicularly  to  the  plane  of  the 
orbit,  causing  periodic  perturbations  in  latitude,  secular 
2  B2 


18  VARIATION  IN  THE  INCLINATION.        SECT.  III. 

variations  in  the  inclination  of  the  oibit,  and  a  retrograde 
motion  to  its  nodes  on  the  true  plane  of  the  ecliptic 
(N.  71).  This  force  tends  to  pull  the  disturbed  body 
above,  or  push  (N.  72)  it  below,  the  plane  of  its  orb.t, 
according  to  the  relative  pos.tions  of  the  two  planets  with 
regard  to  the  sun,  considered  to  be  fixed.  By  this 
action,  it  sometimes  makes  the  plane  of  the  orbit  of  the 
disturbed  body  tend  to  coincide  with  the  plane  of  the 
ecliptic,  and  sometimes  increases  its  inclination  to  that 
plane.  In  consequence  of  which,  its  nodes  alternately 
recede  or  advance  on  the  ecliptic  (N.  73).  When  the 
disturbing  planet  is  in  the  line  of  the  disturbed  planet's 
nodes  (N.  74),  it  neither  affects  these  points,  the  latitude, 
nor  the  inclination,  because  both  planets  are  then  in  the 
same  plane.  When  it  is  at  right  angles  to  the  line  of 
the  nodes,  and  the  orbit  symmetrical  on  each  side  of  the 
disturbing  force,  the  average  motion  of  these  points, 
after  a  revolution  of  the  disturbed  body,  is  retrograde, 
and  comparatively  rapid  ;  but  when  the  disturbing  planet 
is  so  situated  that  the  orbit  of  the  disturbed  planet  is  not 
symmetrical  on  each  side  of  the  disturbing  force,  which 
is  most  frequently  the  case,  every  possible  variety  of 
action  takes  place.  Consequently,  the  nodes  are  per- 
petually advancing  or  receding  with  unequal  velocity ; 
but,  as  a  compensation  is  not  effected,  their  motion  is, 
on  the  whole,  retrograde. 

With  regard  to  the  variations  in  the  inclination,  it  is 
clear,  that,  when  the  orbit  is  symmetrical  on  each  side 
of  the  disturbing  force,  all  its  variations  are  compensated 
after  a  revolution  of  the  disturbed  body,  and  are  merely 
periodical  perturbations  in  the  planet's  latitude  ;  and  no 
secular  change  is  induced  in  the  inclination  of  the  orbit. 
When,  on  the  contrary,  that  orbit  is  not  symmetrical  on 
each  side  of  the  disturbing  force,  although  many  of  the 
variations  in  latitude  are  transient  or  periodical,  still, 
after  a  complete  revolution  of  the  disturbed  body,  a 
portion  remains  uncompensated,  which  forms  a  secular 
change  in  the  inclination  of  the  orbit  to  the  plane  of  the 
ecliptic.  It  is  true,  part  of  this  secular  change  in  the 
inclination  is  compensated  by  the  revolution  of  the  dis- 
turbing body,  whose  motion  has  not  hitherto  been  taken 
into  the  account,  so  that  perturbation  compensates  per- 


SKCT.  III.         MEAN  MOTION  AND  MAJOR  AXIS.  19 

turbation ;  but  still,  a  comparatively  permanent  change 
is  effected  in  the  inclination,  which  is  not  compensated 
till  the  nodes  have  accomplished  a  complete  revolution. 

The  changes  in  the  inclination  are  extremely  minute 
(N.  75),  compared  with  the  motion  of  the  nodes,  and 
there  is  the  same  kind  of  inseparable  connection  between 
their  secular  changes  that  there  is  between  the  variation 
of  the  eccentricity  and  the  motion  of  the  major  axis. 
The  nodes  and  inclinations  vary  simultaneously,  their 
periods  are  the  same,  and  very  great.  The  nodes  of 
Jupiter's  orbit,  from  the  action  of  Saturn  alone,  require 
36,261  years  to  accomplish  even  a  tropical  revolution. 
In  what  precedes,  the  influence  of  only  one  disturbing 
body  has  been  considered  ;  but  when  the  action  and  re- 
action of  the  whole  system  is  taken  into  account,  every 
planet  is  acted  upon,  and  does  itself  act,  in  this  manner, 
on  all  the  others ;  and  the  joint  effect  keeps  the  incli- 
nations and  eccentricities  in  a  state  of  perpetual  variation. 
It  makes  the  major  axis  of  all  the  orbits  continually  re- 
volve, and  causes,  on  an  average,  a  retrograde  motion  of 
the  nodes  of  each  orbit  upon  every  other.  The  ecliptic 
(N.  71)  itself  is  in  motion  from  the  mutual  action  of  the 
earth  and  planets,  so  that  the  whole  is  a  compound  phe- 
nomenon of  great  complexity,  extending  through  un- 
known ages.  At  the  present  time  the  inclinations  of  all 
the  orbits  are  decreasing,  but  so  slowly,  that  the  incli- 
nation of  Jupiter's  orbit  is  only  about  six  minutes  less 
than  it  was  in  the  age  of  Ptolemy. 

But,  in  the  midst  of  all  these  vicissitudes,  the  length 
of  the  major  axis  and  the  mean  motions  of  the  planets 
remain  permanently  independent  of  secular  changes. 
They  are  so  connected  by  Kepler's  law,  of  the  squares 
of  the  periodic  times  being  proportional  to  the  cubes  of 
the  mean  distances  of  the  planets  from  the  sun,  that  one 
cannot  vary  without  affecting  the  other.  And  it  is 
proved,  that  any  variations  which  do  take  place  are 
transient,  and  depend  only  on  the  relative  positions  of 
the  bodies. 

It  is  true  that,  according  to  theory,  the  radial  disturb- 
ing force  should  permanently  alter  the  dimensions  of  all 
the  orbits,  and  the  periodic  times  of  all  the  planets,  to  a 
certain  degree.  For  example,  the  masses  of  all  the 


20  STABILITY  OF  THE  SYSTEM.  SBCT.  HI. 

planets  revolving  within  the  orbit  of  any  one,  such  as 
Mars,  by  adding  to  the  interior  mass,  increase  the  at- 
tracting force  of  the  sun,  which,  therefore,  must  con- 
tract the  dimensions  of  the  orbit  of  that  planet,  and  di- 
minish its  periodic  time  ;  while  the  planets  exterior  to 
Mars'  orbit  must  have  the  contrary  effect.  But  the 
mass  of  the  whole  of  the  planets  and  satellites  taken  to- 
gether is  so  small,  when  compared  with  that  of  the  sun, 
that  these  effects  are  quite  insensible,  and  could  only 
have  been  discovered  by  theory.  And,  as  it  is  certain 
that  the  length  of  the  major  axes  and  the  mean  motions 
are  not  permanently  changed  by  any  other  power  what- 
ever, it  may  be  concluded  that  they  are  invariable. 

With  the  exception  of  these  two  elements,  it  appears 
that  all  the  bodies  are  in  motion,  and  every  orbit  in  a 
state  of  perpetual  change.  Minute  as  these  changes 
are,  they  might  be  supposed  to  accumulate  in  the  course 
of  ages,  sufficiently  to  derange  the  whole  order  of  na- 
ture, to  alter  the  relative  positions  of  the  planets,  to  put 
an  end  to  the  vicissitudes  of  the  seasons,  and  to  bring 
about  collisions  which  would  involve  our  whole  system, 
now  so  harmonious,  in  chaotic  confusion.  It  is  natural 
to  inquire,  what  proof  exists  that  nature  will  be  pre- 
served from  such  a  catastrophe  ?  Nothing  can  be  known 
from  observation,  since  the  existence  of  the  human  race 
has  occupied  comparatively  but  a  point  in  duration, 
while  these  vicissitudes  embrace  myriads  of  ages.  The 
proof  is  simple  and  conclusive.  All  the  variations  of 
the  solar  system,  secular  as  well  as  periodic,  are  ex- 
pressed analytically  by  the  sines  and  cosines  of  circular 
arcs  (N.  76),  which  increase  with  the  time  ;  and,  as  a 
sine  or  cosine  can  never  exceed  the  radius,  but  must 
oscillate  between  zero  and  unity,  however  much  the 
time  may  increase,  it  follows  that,  when  the  variations 
have  accumulated  to  a  maximum,  by  slow  changes,  in 
however  long  a  time,  they  decrease,  by  the  same  slow 
degrees,  till  they  arrive  at  their  smallest  value,  again  to 
begin  a  new  course ;  thus  forever  oscillating  about  a 
mean  value.  This  circumstance,  however,  would  be 
insufficient,  were  it  not  for  the  small  eccentricities  of 
the  planetary  orbits,  their  minute  inclinations  to  the 
plane  of  the  ecliptic,  and  the  revolutions  of  all  the  bodies, 


SKCT.  HI.  STABILITY  OF  THE  SYSTEM.  21 

as  well  planets  as  satellites,  in  the  same  direction. 
These  secure  the  perpetual  stability  of  the  solar  system 
(N.  77).  The  equilibrium,  however,  would  be  de- 
ranged, if  the  planets  moved  in  a  resisting  medium 
(N.  78)  sufficiently  dense  to  diminish  their  tangential 
velocity,  for  then  both  the  eccentricities  and  the  major 
axes  of  the  orbits  would  vary  with  the  time,  so  that  the 
stability  of  the  system  would  be  ultimately  destroyed. 
The  existence  of  an  ethereal  fluid  is  now  proved ;  and 
although  it  is  so  extremely  rare  that  hitherto  its  effects 
on  the  motions  of  the  planets  have  been  altogether  in- 
sensible, there  can  be  no  doubt  that,  in  the  immensity 
of  time,  it  will  modify  the  forms  of  the  planetary  orbits, 
and  may  at  last  even  cause  the  destruction  of  our  sys- 
tem, which  in  itself  contains  no  principle  of  decay,  unless 
a  rotatory  motion  from  west  to  east  has  been  given  to  this 
fluid  by  the  bodies  of  the  solar  system,  which  have  all 
been  revolving  about  the  sun  in  that  direction  for  un- 
known ages.  This  rotation,  which  seems  to  be  highly 
probable,  may  even  have  been  coeval  with  its  creation. 
Such  a  vortex  would  have  no  effect  on  bodies  moving 
with  it,  but  it  would  influence  the  motions  of  those  re- 
volving in  a  contraiy  direction.  It  is  possible  that  the 
disturbances  experienced  by  comets  which  have  already 
revealed  the  existence  of  this  fluid,  may  also,  in  time, 
disclose  its  rotatory  motion. 

The  form  and  position  of  the  planetary  orbits,  and  the 
motion  of  the  bodies  in  the  same  direction,  together  with 
the  periodicity  of  the  terms  in  which  the  inequalities 
are  expressed,  assure  us  that  the  variations  of  the  sys- 
tem are  confined  within  very  narrow  limits,  and  that, 
although  we  do  not  know  the  extent  of  the  limits,  nor 
the  period  of  that  grand  cycle  which  probably  embraces 
millions  of  years,  yet  they  never  will  exceed  what  is 
requisite  for  the  stability  and  harmony  of  the  whole,  for 
the  preservation  of  which  every  circumstance  is  so  beau- 
tifully and  wonderfully  adapted. 

The  plane  of  the  ecliptic  itself,  though  assumed  to  be 
fixed  at  a  given  epoch  for  the  convenience  of  astronomi- 
cal computation,  is  subject  to  a  minute  secular  variation 
of  45"-7,  occasioned  by  the  reciprocal  action  of  the  plan- 
ets. But,  as  this  is  also  periodical,  and  cannot  exceed 


22  INVARIABLE  PLANE.  SECT.  III. 

2°  42',  the  terrestrial  equator,  which  is  inclined  to  it  at 
an  angle  of  23°  27'  34"- 69,  will  never  coincide  with  the 
plane  of  the  ecliptic  :  so  there  never  can  be  perpetual 
spring  (N.  79).  The  rotation  of  the  earth  is  uniform ; 
therefore  day  and  night,  summer  and  winter,  will  con- 
tinue their  vicissitudes  while  the  system  endures,  or  is 
undisturbed  by  foreign  causes. 

"  Yonder  starry  sphere 
Of  planets  and  of  fix'd,  in  all  her  wheels 
Resembles  nearest  mazes  intricate, 
Eccentric,  intervolved,  yet  regular, 
Then  most,  when  most  irregular  they  seem." 

The  stability  of  our  system  was  established  by  La 
Grange:  "a  discovery,"  says  Professor  Playfair,  "that 
must  render  the  name  forever  memorable  in  science, 
and  revered  by  those  who  delight  in  the  contemplation 
of  whatever  is  excellent  and  sublime."  After  Newton's 
discovery  of  the  mechanical  laws  of  the  elliptical  orbits 
of  the  planets,  La  Grange's  discovery  of  their  periodical 
inequalities  is,  without  doubt,  the  noblest  truth  in  physi- 
cal astronomy ;  and  in  respect  of  the  doctrine  of  final 
causes,  it  may  be  regarded  as  the  greatest  of  all. 

Notwithstanding  the  permanency  of  our  system,  the 
secular  variations  in  the  planetary  orbits  would  have 
been  extremely  embarrassing  to  astronomers  when  it 
became  necessary  to  compare  observations  separated  by 
long  periods.  The  difficulty  was  in  part  obviated,  and 
the  principle  for  accomplishing  it  established,  by  La 
Place,  and  has  since  been  extended  by  M.  Poinsot.  It 
appears  that  there  exists  an  invariable  plane  (N.  80), 
passing  through  the  center  of  gravity  of  the  system, 
about  which  the  whole  oscillates  within  very  narrow 
limits,  and  that  this  plane  will  always  remain  parallel  to 
itself,  whatever  changes  time  may  induce  in  the  orbits 
of  the  planets,  in  the  plane  of  the  elliptic,  or  even  in 
the  law  of  gravitation;  provided  only  that  our  system 
remains  unconnected  with  any  other.  The  position  of 
the  plane  is  determined  by  this  property — that,  if  each 
particle  in  the  system  be  multiplied  by  the  area  de- 
scribed upon  this  plan  in  a  given  time,  by  the  projection 
of  its  radius  vector  about  the  common  center  of  gravity 
of  the  whole,  the  sum  of  all  these  products  will  be  a 


SECT.  III.  INVARIABLE  PLANE.  23 

maximum  (N.  81).  La  Place  found  that  the  plane  in 
question  is  inclined  to  the  ecliptic  at  an  angle  of  nearly 
1°  34'  15",  and  that,  in  passing  through  the  sun,  and 
about  midway  between  the  orbits  of  Jupiter  and  Saturn, 
it  may  be  regarded  as  the  equator  of  the  solar  system, 
dividing  it  into  two  parts,  wh.ch  balance  one  another  in 
all  their  motions.  This  plane  of  greatest  inertia,  by  no 
means  peculiar  to  the  solar  system,  but  existing  in  every 
system  of  bodies  submitted  to  their  mutual  attractions 
only,  always  maintains  a  fixed  position,  whence  the 
oscillations  of  the  system  may  be  estimated  through 
unlimited  time.  Future  astronomers  will  know,  from 
its  immutability  or  variation,,  whether  the  sun  and  his 
attendants  are  connected  or  not  w.th  the  other  systems 
of  the  universe.  Should  there  be  no  link  between  them, 
it  in.-iy  be  interred,  from  the  rotation  of  the  sun,  that 
the  center  of  gravity  (N.  82)  of  the  system  situate  within 
his  mass  describes  a  straight  line  in  this  invariable  plane 
or  great  equator  of  the  solar  system,  which,  unaffected 
by  the  changes  of  time,  will  maintain  its  stability  through 
endless  ages.  But,  if  the  fixed  stars,  comets,  or  any 
unknown  and  unseen  bodies,  affect  our  sun  and  planets, 
the  nodes  of  th  s  plane  w.ll  slowly  recede  on  the  plane 
of  that  immense  orbit  which  the  sun  may  describe  about 
some  most  distant  center,  in  a  period  which  it  transcends 
the  powers  of  man  to  determine.  There  is  every  rea- 
son to  believe  that  this  is  the  case  ;  for  it  is  more  than 
probable  that,  remote  as  the  fixed  stars  are,  they  in 
some  degree  influence  our  system,  and  that  even  the 
invariabiLty  of  this  plane  is  relative,  only  appearing  fixed 
to  creatures  incapable  of  estimating  its  minute  and  slow 
changes  during  the  small  extent  of  time  and  space  grant- 
ed to  the  human  race.  "•  The  development  of  such 
changes,"  as  M.  Poinsot  justly  observes,  "  is  similar  to 
an  enormous  curve,  of  which  we  see  so  small  an  arc, 
that  we  imagine  it  to  be  a  straight  line."  If  we  raise 
our  views  to  the  whole  extent  of  the  universe,  and  con- 
sider the  stars,  together  w.th  the  sun,  to  be  wandering 
bodies,  revolving  about  the  common  center  of  creation, 
we  may  then  recognize  in  the  equatorial  plane  passing 
through  the  center  of  gravity  of  the  universe  the  only 
instance  of  absolute  and  eternal  repose. 


24  INEQUALITY  OF  JUPITER  AND  SATURN.      SECT.  III. 

All  the  periodic  and  secular  inequalities  deduced  from 
the  law  of  gravitation  are  so  perfectly  confirmed  by 
observation,  that  analysis  has  become  one  of  the  most 
certain  means  of  discovering  the  planetary  irregularities, 
either  when  they  are  too  small,  or  too  long  in  their 
periods,  to  be  detected  by  other  methods.  Jupiter  and 
Saturn,  however,  exhibit  inequalities  which  for  a  long 
time  seemed  discordant  with  that  law.  All  observations, 
from  those  of  the  Chinese  and  Arabs  down  to  the  pres- 
ent day,  prove  that  for  ages  the  mean  motions  of  Jupiter 
and  Saturn  have  been  affected  by  a  great  inequality  of 
a  very  long  period,  forming  an  apparent  anomaly  in  the 
theory  of  the  planets.  It  was  long  known  by  observa- 
tion that  five  times  the  mean  motion  of  Saturn  is  nearly 
equal  to  twice  that  of  Jupiter  :  a  relation  which  the 
sagacity  of  La  Place  perceived  to  be  the  cause  of  a 
periodic  irregularity  in  the  mean  motion  of  each  of  these 
planets,  which  completes  its  period  in  nearly  918  years, 
the  one  being  retarded  while  the  other  is  accelerated ; 
but  both  the  magnitude  and  period  of  these  quantities 
vary  in  consequence  of  the  secular  variations  in  the 
elements  of  the  orbits.  Suppose  the  two  planets  to  be 
on  the  same  side  of  the  sun,  and  all  three  in  the  same 
straight  line,  they  are  then  said  to  be  in  conjunction 
(N.  83).  Now,  if  they  begin  to  move  at  the  same  time, 
one  making  exactly  five  revolutions  in  its  orbit,  while  the 
other  only  accomplishes  two,  it  is  clear  that  Saturn,  the 
slow-moving  body,  will  only  have  got  through  a  part  of 
its  orbit  during  the  time  that  Jupiter  has  made  one 
whole  revolution  and  part  of  another,  before  they  be 
again  in  conjunction.  It  is  found  that  during  this  time 
their  mutual  action  is  such  as  to  produce  a  great  many 
perturbations  which  compensate  each  other,  but  that 
there  still  remains  a  portion  outstanding,  owing  to  the 
length  of  time  during  which  the  forces  act  in  the  same 
manner  ;  and  if  the  conjunction  always  happened  in  the 
same  point  of  the  orbit,  this  uncompensated  inequality 
in  the  mean  motion  would  go  on  increasing  till  the  peri- 
odic times  and  forms  of  the  orbits  were  completely  and 
permanently  changed :  a  case  that  would  actually  take 
place  if  Jupiter  accomplished  exactly  five  revolutions  in 
the  time  Saturn  performed  two.  These  revolutions 


SICT.  Ill         ACTION  OP  PLANETS  ON  SATELLITES.  25 

are,  however,  not  exactly  commensurable ;  the  points  in 
which  the  conjunctions  take  place  are  in  advance  each 
time  as  much  as  8°*37  ;  so  that  the  conjunctions  do  not 
happen  exactly  in  the  same  points  of  the  orbits  till  after 
a  period  of  850  years;  and,  in  consequence  of  this  small 
advance,  the  planets  are  brought  into  such  relative  posi- 
tions that  the  inequality  which  seemed  to  threaten  the 
stability  of  the  system  is  completely  compensated,  and 
the  bodies,  having  returned  to  the  same  relative  positions 
with  regard  to  one  another  and  the  sun,  begin  a  new 
course.  The  secular  variations  in  the  elements  of  the 
orbit  increase  the  period  of  the  inequality  to  918  years 
(N.  84).  As  any  perturbation  which  affects  the  mean 
motion  affects  also  the  major  axis,  the  disturbing  forces 
tend  to  diminish  the  major  axis  of  Jupiter's  orbit  and 
increase  that  of  Saturn's  during  one  half  of  the  period, 
and  the  contrary  during  the  other  half.  This  inequality 
is  strictly  periodical,  since  it  depends  upon  the  configura- 
tion (N.  85)  of  the  two  planets ;  and  theory  is  confirmed 
by  observation,  which  shows  that,  in  the  course  of  twenty 
centuries,  Jupiter's  mean  motion  has  been  accelerated 
by  about  3°  23',  and  Saturn's  retarded  by  5°  13'.  Sev- 
eral instances  of  perturbations  of  this  kind  occur  in  the 
solar  system.  One,  in  the  mean  motions  of  the  Earth 
and  Venus,  only  amounting  to  a  few  seconds,  has  been 
recently  worked  out  with  immense  labor  by  Professor 
Airy.  It  accomplishes  its  changes  in  240  years,  and 
arises  from  the  circumstance  of  thirteen  times  the  peri- 
odic time  of  Venus  being  nearly  equal  to  eight  times 
that  of  the  Earth.  Small  as  it  is,  it  is  sensible  in  the 
motions  of  the  Earth. 

It  might  be  imagined  that  the  reciprocal  action  of  such 
planets  as  have  satellites  would  be  different  from  the 
influence  of  those  that  have  none.  But  the  distances  of 
the  satellites  from  their  primaries  are  incomparably  less 
than  the  distances  of  the  planets  from  the  sun,  and  from 
one  another;  so  that  the  system  of  a  planet  and  its 
satellites  moves  nearly  as  if  all  these  bodies  were  united 
in  their  common  center  of  gravity.  The  action  of  the 
sun,  however,  in  some  degree  disturbs  the  motion  of  the 
satellites  about  their  primary. 

C 


26  THEORY  OF  JUPITER'S  SATELLITES.       SECT.  IV. 


SECTION  IV. 

Theory  of  Jupiter's  Satellites — Effects  of  the  Figure  of  Jupiter  upon  his 
Satellites — Position  of  theif  Orbits — Singular  Laws  among-  the  Motions 
of  the  first  three  Satellites — Eclipses  of  the  Satellites — Velocity  of  Light 
— Aberration — Ethereal  Medium — Satellites  of  Saturn  and  Uranus. 

THE  changes  which  take  place  in  the  planetary  sys- 
tem are  exhibited  on  a  smaller  scale  by  Jupiter  and  his 
satellites ;  and,  as  the  period  requisite  for  the  develop- 
ment of  the  inequalities  of  these  moons  only  extends  to 
a  few  centuries,  it  may  be  regarded  as  an  epitome  of 
that  grand  cycle  which  will  not  be  accomplished  by  the 
planets  in  myriads  of  ages.  The  revolutions  of  the 
satellites  about  Jupiter  are  precisely  similar  to  those  of 
the  planets  about  the  sun  :  it  is  true  they  are  disturbed 
by  the  sun,  but  his  distance  is  so  great,  that  their 
motions  are  nearly  the  same  as  if  they  were  not  under 
his  influence.  The  satellites,  like  the  planets,  were 
probably  projected  in  elliptical  orbits  :  but,  as  the  masses 
of  the  satellites  are  nearly  100,000  times  less  than  that 
of  Jupiter ;  and  as  the  compression  of  Jupiter's  sphe- 
roid is  so  great,  in  consequence  of  his  rapid  rotation, 
that  his  equatorial  diameter  exceeds  his  polar  diameter 
by  no  less  than  6000  miles ;  the  immense  quantity  of 
prominent  matter  at  his  equator  must  soon  have  given 
the  circular  form  observed  in  the  orbits  of  the  first  and 
second  satellites,  which  its  superior  attraction  will  al- 
ways maintain.  The  third  and  fourth  satellites,  being 
farther  removed  from  its  influence,  revolve  in  orbits 
with  a  very  small  eccentricity.  And  although  the  first 
two  sensibly  move  in  circles,  their  orbits  acquire  a 
small  ellipticity,  from  the  disturbances  they  experience 
(N.  86). 

It  has  been  stated,  that  the  attraction  of  a  sphere  on 
an  exterior  body  is  the  same  as  if  its  mass  were  united 
in  one  particle  in  its  center  of  gravity,  and  therefore 
inversely  as  the  square  of  the  distance.  In  a  spheroid, 
however,  there  is  an  additional  force  arising  from  the 
bulging  mass  at  its  equator,  which,  not  following  the 
exact  law  of  gravity,  acts  as  a  disturbing  force.  One 


SECT.  IV.     EFFECTS  OF  JUPITER'S  COMPRESSION.  27 

effect  of  this  disturbing  force  in  the  spheroid  of  Jupiter 
is,  to  occasion  a  direct  "motion  in  the  greater  axes  of  the 
orbits  of  all  his  satellites,  which  is  more  rapid  the 
nearer  the  satellite  is  to  the  planet,  and  very  much 
greater  than  that  part  of  their  motion  which  arises  from 
the  disturbing  action  of  the  sun.  The  same  cause 
occasions  the  orbits  of  the  satellites  to  remain  nearly  in 
tho  plane  of  Jupiter's  equator  (N.  87),  on  account  of 
which  the  satellites  are  always  seen  nearly  in  the  same 
line  (N.  88) ;  and  the  powerful  action  of  that  quantity 
of  prominent  matter  is  the  reason  why  the  motions  of 
the  nodes  of  these  small  bodies  are  so  much  more  rapid 
than  those  of  the  planet.  The  nodes  of  the  fourth 
satellite  accomplish  a  tropical  revolution  in  531  years ; 
while  those  of  Jupiter's  orbit  require  no  less  than 
36,261  years ; — a  proof  of  the  reciprocal  attraction  be- 
tween each  particle  of  Jupiter's  equator  and  of  the 
satellites.  In  fact,  if  the  satellites  moved  exactly  in  the 
plane  of  Jupiter's  equator,  they  would  not  be  pulled 
out  of  that  plane,  because  his  attraction  would  be  equal 
on  both  sides  of  it.  But,  as  their  orbits  have  a  small 
inclination  to  the  plane  of  the  planet's  equator,  there 
is  a  want  of  symmetry,  and  the  action  of  the  protuberant 
matter  tends  to  make  the  nodes  regress  by  pulling  the 
satellites  above  or  below  the  planes  of  their  orbits ;  an 
action  which  is  so  great  on  the  interior  satellites,  that 
the  motions  of  their  nodes  are  nearly  the  same  as  if  no 
other  disturbing  force  existed. 

The  orbits  of  the  satellites  do  not  retain  a  permanent 
inclination,  either  to  the  plane  of  Jupiter's  equator,  or 
to  that  of  his  orbit,  but  to  certain  planes  passing  between 
the  two,  and  through  their  intersection.  These  have  a 
greater  inclination  to  his  equator  the  farther  the  satel- 
lite is  removed,  owing  to  the  influence  of  Jupiter's 
compression ;  and  they  have  a  slow  motion  correspond- 
ing to  secular  variations  in  the  planes  of  Jupiter's  orbit 
and  equator. 

The  satellites  are  not  only  subject  to  periodic  and 
secular  inequalities  from  their  mutual  attraction,  similar 
to  those  which  affect  the  motions  and  orbits  of  the 
planets,  but  also  to  others  peculiar  to  themselves.  Of 
the  periodic  inequalities  arising  from  their  mutual  at- 


28  PERTURBATIONS  OF  THE  SATELLITES.    SECT.  IV. 

traction,  the  most  remarkable  take  place  in  the  angular 
motions  (N.  89)  of  the  three  nearest  to  Jupiter,  the 
second  of  which  receives  from  the  first  a  perturbation 
similar  to  that  which  it  produces  in  the  third  ;  and  it 
experiences  from  the  third  a  perturbation  similar  to  that 
which  it  communicates  to  the  first.  In  the  eclipses 
these  two  inequalities  are  combined  into  one,  whose 
period  is  437-659  da>'s.  The  variations  peculiar  to  the 
satellites  arise  from  the  secular  inequalities  occasioned 
by  the  action  of  the  planets  in  the  form  and  position  of 
Jupiter's  orbit,  and  from  the  displacement  of  his  equator. 
It  is  obvious  that  whatever  alters  the  relative  positions 
of  the  sun,  Jupiter,  and  his  satellites,  must  occasion  a 
change  in  the  directions  and  intensities  of  the  forces, 
which  will  affect  the  motions  and  orbits  of  the  satellites. 
For  this  reason  the  secular  variations  in  the  eccen- 
tricity of  Jupiter's  orbit  occasion  secular  inequalities  in 
the  mean  motions  of  the  satellites,  and  in  the  motions 
of  the  nodes  and  apsides  of  their  orbits.  The  displace- 
ment of  the  orbit  of  Jupiter,  and  the  variation  in  the 
position  of  his  equator,  also  aflfect  these  small  bodies 
(N.  90).  The  plane  of  Jupiter's  equator  is  inclined  to 
the  plane  of  his  orbit  at  an  angle  of  3°  5'  30",  so  that 
the  action  of  the  sun  and  of  the  satellites  themselves 
produces  a  nutation  and  precession  (N.  91)  in  his  equa- 
tor, precisely  similar  to  that  which  takes  place  in  the 
rotation  of  the  earth,  from  the  action  of  the  sun  and 
moon.  Hence  the  protuberant  matter  at  Jupiter's  equa- 
tor is  continually  changing  its  position  with  regard  to 
the  satellites,  and  produces  corresponding  mutations  in 
their  motions.  And,  as  the  cause  must  be  proportional 
to  the  effect,  these  inequalities  afford  the  means,  not 
only  of  ascertaining  the  compression  of  Jupiter's  sphe- 
roid, but  they  prove  that  his  mass  is  not  homogeneous. 
Although  the  apparent  diameters  of  the  satellites  are 
too  small  to  be  measured,  yet  their  perturbations  give 
the  values  of  their  masses  with  considerable  accuracy — 
a  striking  proof  of  the  power  of  analysis. 

A  singular  law  obtains  among  the  mean  motions  and 
mean  longitudes  of  the  first  three  satellites.  It  appears 
from  observation  that  the  mean  motion  of  the  first 
satellite,  plus  twice  that  of  the  third,  is  equal  to  three 


SKCT,  IV.  ECLIPSES  OP  THE  SATELLITES.  29 

times  that  of  the  second ;  and  that  the  mean  longitude 
of  the  first  satellite,  minus  three  times  that  of  the 
second,  plus  twice  that  of  the  third,  is  always  equal  to 
two  right  angles.  It  is  proved  by  theory,  that  if  these 
relations  had  only  been  approximate  when  the  satellites 
were  first  launched  into  space,  their  mutual  attractions 
would  have  established  and  maintained  them,  notwith- 
standing the  secular  inequalities  to  which  they  are 
liable.  They  extend  to  the  synodic  motions  (N.  92)  of 
the  satellites ;  consequently  they  affect  then*  eclipses, 
and  have  a  very  great  influence  on  their  whole  theory. 
The  satellites  move  so  nearly  in  the  plane  of  Jupiter's 
equator,  which  has  a  very  small  inclination  to  his  orbit, 
that  the  first  three  are  eclipsed  at  each  revolution  by 
the  shadow  of  the  planet,  which  is  much  larger  than 
the  shadow  of  the  moon :  the  fourth  satellite  is  not 
eclipsed  so  frequently  as  the  others.  The  eclipses 
take  place  close  to  the  disc  of  Jupiter  when  he  is  near 
opposition  (N.  93);  but  at  times  his  shadow  is  so  pro- 
jected with  regard  to  the  earth,  that  the  third  and 
fourth  satellites  vanish  and  reappear  on  the  same  side 
of  the  disc  (N.  94).  These  eclipses  are  in  all  respects 
similar  to  those  of  the  moon :  but,  occasionally,  the 
satellites  eclipse  Jupiter,  sometimes  passing  like  obscure 
spots  across  his  surface,  resembling  annular  eclipses  of 
the  sun,  and  sometimes  like  a  bright  spot  traversing  one 
of  his  dark  belts.  Before  opposition,  the  shadow  of  the 
satelb'te,  like  a  round  black  spot,  precedes  its  passage 
over  the  disc  of  the  planet ;  and  after  opposition,  the 
shadow  follows  the  satellite. 

In  consequence  of  the  relations  already  mentioned  in 
the  mean  motions  and  mean  longitudes  of  the  first  three 
satellites,  they  never  can  be  all  eclipsed  at  the  same 
time.  For  when  the  second  and  third  are  in  one  direc- 
tion, the  first  is  in  the  opposite  direction ;  consequently, 
when  the  first  is  eclipsed,  the  other  two  must  be  be- 
tween the  sun  and  Jupiter.  The  instant  of  the  begin- 
ning or  end  of  an  eclipse  of  a  satellite  marks  the  same 
instant  of  absolute  time  to  all  the  inhabitants  of  the 
earth;  therefore,  the  time  of  these  eclipses  observed 
by  a  traveler,  when  compared  with  the  time  of  the 
eclipse  computed  for  Greenwich,  or  any  other  fixed 
c2 


30  ABERRATION.  SECT.  IV. 

meridian  (N.  95),  gives  the  difference  of  the  meridians 
in  time,  and,  consequently,  the  longitude  of  the  place  of 
observation.  The  eclipses  of  Jupiter's  satellites  have 
been  the  means  of  a  discovery  which,  though  not  so 
immediately  applicable  to  the  wants  of  man,  unfolds 
one  of  the  properties  of  light — that  medium  without 
whose  cheering  influence  all  the  beauties  of  the  creation 
would  have  been  to  us  a  blank.  It  is  observed,  that 
those  eclipses  of  the  first  satellite,  which  happen  when 
Jupiter  is  near  conjunction  (N.  96),  are  later  by  16m 
26"6  than  those  which  take  place  when  the  planet  is  in 
opposition.  As  Jupiter  is  nearer  to  us  when  in  opposi- 
tion by  the  whole  breadth  of  the  earth's  orbit  than 
when  in  conjunction,  this  circumstance  is  attributed  to 
the  time  employed  by  the  rays  of  light  in  crossing  the 
earth's  orbit,  a  distance  of  about  191X000,000  of  miles  ; 
whence  it  is  estimated  that  light  travels  at  the  rate  of 
190,000  miles  in  one  second.  Such  is  its  velocity,  that 
the  earth,  moving  at  the  rate  of  nineteen  miles  in  a 
second,  would  take  two  months  to  pass  through  a  dis- 
tance which  a  ray  of  light  would  dart  over  in  eight 
minutes.  The  subsequent  discovery  of  the  aberration 
of  light  confirmed  this  astonishing  result. 

Objects  appear  to  be  situated  in  the  direction  of  the 
rays  which  proceed  from  them.  Were  light  propagated 
instantaneously,  every  object,  whether  at  rest  or  in  mo- 
tion, would  appear  in  the  direction  of  these  rays  ;  but 
as  light  takes  some  time  to  travel,  we  see  Jupiter  in 
conjunction,  by  means  of  rays  that  left  him  16m  268>6  be- 
fore ;  but,  during  that  time,  we  have  changed  our  posi- 
tion, in  consequence  of  the  motion  of  the  earth  in  its 
orbit :  we  therefore  refer  Jupiter  to  a  place  in  which  he 
is  not.  His  true  position  is  in  the  diagonal  (N.  97)  of 
the  parallelogram,  whose  sides  are  in  the  ratio  of  the 
velocity  of  light  to  the  velocity  of  the  earth  in  its  orbit, 
which  is  as  190,000  to  19,  or  10,000  to  1.  In  conse- 
quence of  the  aberration  of  light,  the  heavenly  bodies 
seem  to  be  in  places  in  which  they  are  not.  In  fact,  if 
the  earth  were  at  rest,  rays  from  a  star  would  pass  along 
the  axis  of  a  telescope  directed  to  it;  but  if  the  earth 
were  to  begin  to  move  in  its  orbit,  with  its  usual  velocity, 
these  rays  would  strike  against  the  side  of  the  tube ;  it 


SKCT.  IV.  VELOCITY  OF  LIGHT.  31 

would,  therefore,  be  necessary  to  incline  the  telescope 
a  little,  in  order  to  see  the  star.  The  angle  contained 
between  the  axis  of  the  telescope  and  a  line  drawn  to 
the  true  place  of  the  star,  is  its  aberration,  which  varies 
in  quantity  and  direction  in  different  parts  of  the  earth's 
orbit ;  but  as  it  is  only  20"-36,  it  is  insensible  in  ordinary 
cases  (N.  98). 

The  velocity  of  light  deduced  from  the  observed  aber- 
ration of  the  fixed  stars  perfectly  corresponds  with  that 
given  by  the  eclipses  of  the  first  satellite.  The  same 
result,  obtained  from  sources  so  different,  leaves  not  a 
doubt  of  its  truth.  Many  such  beautiful  coincidences, 
derived  from  circumstances  apparently  the  most  un- 
promising and  dissimilar,  occur  in  physical  astronomy, 
and  prove  connections  which  we  might  otherwise  be  un- 
able to  trace.  The  identity  of  the  velocity  of  light,  at 
the  distance  of  Jupiter,  and  on  the  earth's  surface,  shows 
that  its  velocity  is  uniform  ;  and  if  light  consists  in  the 
vibrations  of  an  elastic  fluid  or  ether  filling  space,  a  hy- 
pothesis which  accords  best  with  observed  phenomena, 
the  uniformity  of  its  velocity  shows  that  the  density 
of  the  fluid  throughout  the  whole  extent  of  the  solar 
system  must  be  proportional  to  its  elasticity  (N.  99). 
Among  the  fortunate  conjectures  which  have  been  con- 
firmed by  subsequent  experience,  that  of  Bacon  is  not 
the  least  remarkable.  "  It  produces  in  me,"  says  the 
restorer  of  true  philosophy,  "  a  doubt  whether  the  face 
of  the  serene  and  starry  heavens  be  seen  at  the  instant 
it  really  exists,  or  not  till  some  time  later :  and  whether 
there  be  not,  with  respect  to  the  heavenly  bodies,  a  true 
time  and  an  apparent  time,  no  less  than  a  true  place 
and  an  apparent  place,  as  astronomers  say,  on  account 
of  parallax.  For  it  seems  incredible  that  the  species  or 
rays  of  the  celestial  bodies  can  pass  through  the  im- 
mense interval  between  them  and  us  in  an  instant,  or 
that  they  do  not  even  require  some  considerable  portion 
of  time." 

Great  discoveries  generally  lead  to  a  variety  of  con- 
clusions :  the  aberration  of  light  affords  a  direct  proof  of 
the  motion  of  the  earth  in  its  orbit ;  and  its  rotation  is 
proved  by  the  theory  of  falling  bodies,  since  the  centri- 
fugal force  it  induces  retards  the  oscillations  of  the  pen- 


32  SATELLITES  OF  JUPITER  AND  URANUS.    SKCT.  IV. 

dulum  (N.  100)  in  going  from  the  pole  to  the  equator. 
Thus  a  high  degree  of  scientific  knowledge  has  been 
requisite  to  dispel  the  errors  of  the  senses. 

The  little  that  is  known  of  the  theories  of  the  satel- 
lites of  Saturn  and  Uranus,  is,  in  all  respects,  similar  to 
that  of  Jupiter.  Saturn  is  accompanied  by  seven  satel- 
lites, the  most  distant  of  which  is  about  the  size  of  the 
planet  Mars.  Its  orbit  has  a  sensible  inclination  to  the 
plane  of  the  ring ;  but  the  great  compression  of  Saturn 
occasions  the  other  satellites  to  move  nearly  in  the  plane 
of  his  equator.  So  many  circumstances  must  concur  to 
render  the  two  interior  satellites  visible,  that  they  have 
very  rarely  been  seen.  They  move  exactly  at  the  edge 
of  the  ring,  and  their  orbits  never  deviate  from  its  plane. 
In  1789,  Sir  William  Herschel  saw  them,  like  beads, 
threading  the  slender  line  of  light  which  the  ring  is  re- 
duced to,  when  seen  edgewise  from  the  earth.  And 
for  a  short  time  he  perceived  them  advancing  off  it  at 
each  end,  when  turning  round  in  their  orbits.  The 
eclipses  of  the  exterior  satellites  only  take  place  when 
the  ring  is  in  this  position.  Of  the  situation  of  the  equa- 
tor of  Uranus  we  know  nothing,  nor  of  his  compression ; 
but  the  orbits  of  his  satellites  are  nearly  perpendicular 
to  the  plane  of  the  ecliptic ;  and,  by  analogy,  they  ought 
to  be  in  the  plane  of  his  equator.  Uranus  is  so  remote 
that  he  has  more  the  appearance  of  a  planetary  nebula 
than  a  planet,  which  renders  it  extremely  difficult  to 
distinguish  the  satellites  at  all ;  and  quite  hopeless  with- 
out such  a  telescope  as  is  rarely  to  be  met  with  even  in 
observatories.  Sir  William  Herschel  discovered  six, 
and  determined  the  motions  of  two  of  them  ;  but  from 
that  time  the  position  of  the  planet  has  been  such  as  to 
render  farther  observations  impossible.  The  subject 
has  recently  occupied  the  attention  of  his  son,  who  has 
found  evidence  of  the  general  correctness  of  his  father's 
views,  and  has  been  enabled  to  determine  the  elements 
of  the  motions  of  these  minute  objects  with  more  accu- 
racy. The  first  satellite  performs  its  revolution  about 
Uranus  in  8d  16h  56ra  28s-6  ;  and  the  second  satellite  ac- 
complishes its  period  in  13d  llh  7m  12B«6.  The  orbits  of 
both  seem  to  have  an  inclination  of  about  101° -2  to  the 
plane  of  the  ecliptic ;  and  their  motions  offer  the  singu- 


SECT.  V  LUNAR  THEORY  33 

Jar  phenomenon  of  being  retrograde,  or  from  east  to 
west ;  while  all  the  planets  and  the  other  satellites  re- 
volve in  the  contrary  direction.  Sir  John  Herschel  could 
not  perceive  the  smallest  indication  of  a  ring. 


SECTION  V. 

Lunar  Theory — Periodic  Perturbations  of  the  Moon — Equation  of  Center- 
Evection — Variation — Annual  Equation — Direct  and  Indirect  Action  of 
Planets— The  Moon's  Action  on  the  Earth  disturbs  her  own  Motion- 
Eccentricity  and  Inclination  of  Lunar  Orbit  Invariable — Acceleration — 
Secular  Variation  in  Nodes  and  Perigee— Motion  of  Nodes  and  Perigee 
inseparably  connected  with  the  Acceleration — Nutation  of  Lunar  Orbit 
— Form  and  Internal  Structure  of  the  Earth  determined  from  it — Lunar, 
Solar,  and  Planetary  Eclipses— Occultations  and  Lunar  Distances — Mean 
Distance  of  the  Sun  from  the  Earth  obtained  from  Lunar  Theory — Abso- 
lute Distances  of  the  Planets,  how  Found. 

OUR  constant  companion,  the  moon,  next  claims  our 
attention.  Several  circumstances  concur  to  render  her 
motions  the  most  interesting,  and  at  the  same  time  the 
most  difficult  to  investigate,  of  all  the  bodies  of  our  sys- 
tem. In  the  solar  system,  planet  troubles  planet ;  but  in 
the  lunar  theory,  the  sun  is  the  great  disturbing  cause ; 
his  vast  distance  being  compensated  by  his  enormous 
magnitude,  so  that  the  motions  of  the  moon  are  more 
irregular  than  those  of  the  planets ;  and,  on  account  of 
the  great  ellipticity  of  her  orbit,  and  the  size  of  the  sun, 
the  approximations  to  her  motions  are  tedious  and  diffi- 
cult, beyond  what  those  unaccustomed  to  such  investiga- 
tions could  imagine.  The  average  distance  of  the  moon 
from  the  center  of  the  earth  is  only  237,360  miles,  so 
that  her  motion  among  the  stars  is  perceptible  in  a  few 
hours.  She  completes  a  circuit  of  the  heavens  in 
27d  7h  43m  48-7,  moving  in  an  orbit  whose  eccentricity  is 
about  12,985  miles.  The  moon  is  about  four  hundred 
times  nearer  to  the  earth  than  the  sun.  The  proximity 
of  the  moon  to  the  earth  keeps  them  together.  For  so 
great  is  the  attraction  of  the  sun,  that  if  the  moon  were 
farther  from  the  earth,  she  would  leave  it  altogether,  and 
would  revolve  as  an  independent  planet  about  the  sun. 

The  disturbing  action  (N.  101)  of  the  sun  on  the  moon 
is  equivalent  to  three  forces.  The  first,  acting  in  the 
direction  of  the  line  joining  the  moon  and  earth,  in- 
3 


34  DISTURBING  ACTION  OF  THE  SUN.          SECT.  V. 

ereases  or  diminishes  her  gravity  to  the  earth.  The 
second,  acting  in  the  direction  of  a  tangent  to  her  orbit, 
disturbs  her  motion  in  longitude  ;  and  the  .third,  acting 
perpendicularly  to  the  plane  of  her  orbit,  disturbs  her 
motion  in  latitude — that  is,  it  brings  her  nearer  or  re- 
moves her  farther  from  the  plane  of  the  ecliptic  than 
she  would  otherwise  be.  The  periodic  perturbations' 
in  the  moon  arising  from  these  forces,  are  perfectly  sim- 
ilar to  the  periodic  perturbations  of  the  planets.  But 
they  are  much  greater  and  more  numerous ;  because 
the  sun  is  so  large,  that  many  inequalities  which  are 
quite  insensible  in  the  motions  of  the  planets,  are  of 
great  magnitude  in  those  of  the  moon.  Among  the  in- 
numerable periodic  inequalities  to  which  the  moon's 
motion  in  longitude  is  liable,  the  most  remarkable  are, 
the  Equation  of  the  Center,  which  is  the  difference  be- 
tween the  moon's  mean  and  true  longitude,  the  Evec- 
tion,  the  Variation,  and  the  Annual  Equation.  The 
disturbing  force  which  acts  in  the  line  joining  the  moon 
and  earth  produces  the  Evection  :  it  diminishes  the  ec- 
centricity of  the  lunar  orbit  in  conjunction  and  opposi- 
tion, thereby  making  it  more  circular,  and  augments  it 
in  quadrature,  which  consequently  renders  it  more  ellip- 
tical. The  period  of  this  inequality  is  less  than  thirty- 
two  days.  Were  the  increase  and  diminution  always 
the  same,  the  Evection  would  only  depend  upon  the 
distance  of  the  moon  from  the  sun  ;  but  its  absolute 
value  also  varies  with  her  distance  from  the  perigee 
(N.  102)  of  her  orbit.  Ancient  astronomers,  who  ob- 
served the  moon  solely  with  a  view  to  the  prediction  of 
eclipses,  which  can  only  happen  in  conjunction  and  oppo- 
sition, where  the  eccentricity  is  diminished  by  the  Evec- 
tion, assigned  too  small  a  value  to  the  ellipticity  of  her 
orbit  (N.  193).  The  Evection  was  discovered  by  Ptole- 
my from  observation,  about  A.D.  140.  The  variation 
produced  by  the  tangential  disturbing  force,  which  is 
at  its  maximum  when  the  moon  is  45°  distant  from  the 
sun,  vanishes  when  that  distance  amounts  to  a  quadrant, 
and  also  when  the  moon  is  in  conjunction  and  opposi- 
tion ;  consequently,  that  inequality  never  could  have 
been  discovered  from  the  eclipses  :  its  period  is  half  a 
lunar  month  (N.  104).  The  Annual  Equation  depends 


SBCT.  V.     DISTURBING  ACTION  OF  THE  PLANETS.  35 

upon  the  sun's  distance  from  the  earth  :  it  arises  from 
the  moon's  motion  being  accelerated  when  that  of  the 
earth  is  retarded,  and  vice  versa — for  when  the  earth  is 
in  its  perihelion,  the  lunar  orbit  is  enlarged  by  the  ac- 
tion of  the  sun ;  therefore,  the  moon  requires  more 
time  to  perform  her  revolution.  But,  as  the  earth  ap- 
proaches its  aphelion,  the  moon's  orbit  contracts,  and 
less  time  is  necessaiy  to  accomplish  her  motion — its 
period,  consequently,  depends  upon  the  time  of  the 
year.  In  the  eclipses,  the  annual  equation  combines 
with  the  equation  of  the  center  of  the  terrestrial  orbit, 
so  that  ancient  astronomers  imagined  the  earth's  orbit 
to  have  a  greater  eccentricity  than  modern  astronomers 
assign  to  it. 

The  planets  disturb  the  motion  of  the  moon  both 
directly  and  indirectly :  their  action  on  the  earth  alters 
its  relative  position  with  regard  to  the  sun  and  moon, 
and  occasions  inequalities  in  the  moon's  motion,  which 
are  more  considerable  than  those  arising  from  their 
direct  action  ;  for  the  same  reason  the  moon,  by  disturb- 
ing the  earth,  indirectly  disturbs  her  own  motion.  Nei- 
ther the  eccentricity  of  the  lunar  orbit,  nor  its  mean 
inclination  to  the  plane  of  the  ecliptic,  have  experienced 
any  changes  from  secular  inequalities;  for,  although 
the  mean  action  of  the  sun  on  the  moon  depends  upon 
the  inclination  of  the  lunar  orbit  to  the  ecliptic,  and  the 
position  of  the  ecliptic  is  subject  to  a  secular  inequality, 
yet  analysis  shows  that  it  does  not  occasion  a  secular 
variation  in  the  inclination  of  the  lunar  orbit,  because 
the  action  of  the  sun  constantly  brings  the  moon's  orbit 
to  the  same  inclination  to  the  ecliptic.  The  mean  mo- 
tion, the  nodes,  and  the  perigee,  however,  are  subject 
to  very  remarkable  variations. 

From  the  eclipse  observed  by  the  Chaldeans  at  Baby- 
lon, on  the  19th  of  March,  seven  hundred  and  twenty- 
one  years  before  the  Christian  era,  the  place  of  the 
moon  is  known  from  that  of  the  sun  at  the  instant  of 
opposition  (N.  83),  whence  her  mean  longitude  may  be 
found.  But  the  comparison  of  this  mean  longitude  with 
another  mean  longitude,  computed  back  for  the  instant 
of  the  eclipse  from  modern  observations,  shows  that  the 
moon  performs  her  revolution  round  the  earth  more 


36  ACCELERATION.  SECT.  V. 

rapidly  and  in  a  shorter  time  now  than  she  did  formerly, 
and  that  the  acceleration  in  her  mean  motion  has  been 
increasing  from  age  to  age  as  the  square  of  the  time 
(N.  105).  All  ancient  and  intermediate  eclipses  confirm 
this  result.  As  the  mean  motions  of  the  planets  have 
no  secular  inequalities,  this  seemed  to  be  an  unaccount- 
able anomaly.  It  was  at  one  time  attributed  to  the  re- 
sistance of  an  ethereal  medium  pervading  space,  and  at 
another  to  the  successive  transmission  of  the  gravitating 
force.  But  as  La  Place  proved  that  neither  of  these 
causes,  even  if  they  exist,  have  any  influence  on  the 
motions  of  the  lunar  perigee  (N.  102)  or  nodes,  they 
could  not  affect  the  mean  motion ;  a  variation  in  the 
mean  motion  from  such  causes  being  inseparably  con- 
nected with  the  variations  in  the  motions  of  the  perigee 
and  nodes.  That  great  mathematician,  in  studying  the 
theory  of  Jupiter's  satellites,  perceived  that  the  secular 
variation  in  the  elements  of  Jupiter's  orbit,  from  the 
action  of  the  planets,  occasions  corresponding  changes 
in  the  motions  of  the  satellites,  which  led  him  to  sus- 
pect that  the  acceleration  in  the  mean  motion  of  the 
moon  might  be  connected  with  the  secular  variation  in 
the  eccentricity  of  the  terrestrial  orbit.  Analysis  has 
shown  that  he  assigned  the  true  cause  of  the  acceleration. 
It  is  proved  that  the  greater  the  eccentricity  of  the 
terrestrial  orbit,  the  greater  is  the  disturbing  action  of 
the  sun  on  the  moon.  Now  as  the  eccentricity  has 
been  decreasing  for  ages,  the  effect  of  the  sun  in  dis- 
turbing the  moon  has  been  diminishing  during  that  time. 
Consequently  the  attraction  of  the  earth  has  had  a  more 
and  more  powerful  effect  on  the  moon,  and  has  been 
continually  diminishing  the  size  of  the  lunar  orbit.  So 
that  the  moon's  velocity  has  been  gradually  augmenting 
for  many  centuries  to  balance  the  increase  of  the  earth's 
attraction.  This  secular  increase  in  the  moon's  velocity 
is  called  the  Acceleration,  a  name  peculiarly  appropriate 
at  present,  and  which  will  continue  to  be  so  for  a  vast 
number  of  ages ;  because,  as  long  as  the  earth's  eccen- 
tricity diminishes,  the  moon's  mean  motion  will  be  ac- 
celerated ;  but  when  the  eccentricity  has  passed  its 
minimum,  and  begins  to  increase,  the  mean  motion  will 
be  retarded  from  age  to  age.  The  secular  acceleration 


SECT.  V.  MOTION  OF  NODES  AND  PERIGEE.  37 

is  now  about  ll"-9,  but  its  effect  on  the  moon's  place 
increases  as  the  square  of  the  time.  It  is  remarkable 
that  the  action  of  the  planets,  thus  reflected  by  the  sun 
to  the  moon,  is  much  more  sensible  than  their  direct 
action  either  on  the  earth  or  moon.  The  secular  dimi- 
nution in  the  eccentricity,  which  has  not  altered  the 
equation  of  the  center  of  the  sun  by  eight  minutes  since 
the  earliest  recorded  eclipses,  has  produced  a  variation 
of  about  1°  48'  in  the  moon's  longitude,  and  of  7°  12'  in 
her  mean  anomaly  (N.  106). 

The  action  of  the  sun  occasions  a  rapid  but  variable 
motion  in  the  nodes  and  perigee  of  the  lunar  orbit. 
Though  the  nodes  recede  during  the  greater  part  of  the 
moon's  revolution,  and  advance  during  the  smaller,  they 
perform  then*  sidereal  revolution  in  6793d  9h  23ra  9"-3  ; 
and  the  perigee  accomplishes  a  revolution  in  3232J  13h 
48m  29s- 6,  or  a  little  more  thart  nine  years,  notwith- 
standing its  motion  is  sometimes  retrograde  and  some- 
times direct :  but  such  is  the  difference  between  the 
disturbing  energy  of  the  sun  and  that  of  all  the  planets 
put  together,  that  it  requires  no  less  than  109,830  years 
for  the  greater  axis  of  the  terrestrial  orbit  to  do  the 
same,  moving  at  the  rate  of  IT'-S  annually.  The  form 
of  the  earth  has  no  sensible  effect  either  on  the  lunar 
nodes  or  apsides.  It  is  evident  that  the  same  secular 
variation  which  changes  the  sun's  distance  from  the 
earth,  and  occasions  the  acceleration  in  the  moon's  mean 
motion,  must  affect  the  nodes  and  perigee.  It  conse- 
quently appears,  from  theory  as  well  as  observation,  that 
both  these  elements  are  subject  to  a  secular  inequality, 
arising  from  the  variation  in  the  eccentricity  of  the 
earth's  orbit,  which  connects  them  with  the  Acceleration, 
so  that  both  are  retarded  when  the  mean  motion  is  an- 
ticipated. The  secular  variations  in  these  three  ele- 
ments are  in  the  ratio  of  the  numbers  3,  0-735,  and  1 ; 
whence  the  three  motions  of  the  moon,  with  regard  to 
the  sun,  to  her  perigee,  and  to  her  nodes,  are  continu- 
ally accelerated,  and  their  secular  equations  are  as  the 
numbers  1,  4-702,  and  0-612.  A  comparison  of  ancient 
eclipses  observed  by  the  Arabs,  Greeks,  and  Chaldeans, 
imperfect  as  they  are,  with  modern  observations,  con- 
firms these  results  of  analysis.  Future  ages  will  de- 
D 


38  NUTATION  OF  LUNAR  ORBIT.  SECT.  V. 

velop  these  great  inequalities,  which  at  some  most 
distant  period  will  amount  to  many  circumferences 
(N.  107).  They  are,  indeed,  periodic;  but  who  shall 
tell  their  period  ?  Millions  of  years  must  elapse  before 
that  great  cycle  is  accomplished. 

.  The  moon  is  so  near,  that  the  excess  of  matter  at  the 
earth's  equator  occasions  periodic  variations  in  her  lon- 
gitude, and  also  that  remarkable  inequality  in  her  lati- 
tude, already  mentioned  as  a  nutation  in  the  lunar  orbit, 
which  diminishes  its  inclination  to  the  ecliptic  when  the 
moon's  ascending  node  coincides  with  the  equinox  of 
spring,  and  augments  it  when  that  node  coincides  with 
the  equinox  of  autumn.  As  the  cause  must  be  propor- 
tional to  the  effect,  a  comparison  of  these  inequalities, 
computed  from  theory,  with  the  same  given  by  obser- 
vation, shows  that  the  compression  of  the  terrestrial 
spheroid,  or  the  ratio  of  the  difference  between  the 
polar  and  the  equatorial  diameters,  to  the  diameter  of 
the  equator,  is  ^37.7^  It  is  proved  analytically,  that  if 
a  fluid  mass  of  homogeneous  matter,  whose  particles 
attract  each  other  inversely  as  the  squares  of  the  dis- 
tance, were  to  revolve  about  an  axis  as  the  earth  does, 
it  would  assume  the  form  of  a  spheroid  whose  compres- 
sion is  -^1^.  Since  that  is  not  the  case,  the  earth  can- 
not be  Homogeneous,  but  must  decrease  in  density  from 
its  center  to  its  circumference.  Thus  the  moon's 
eclipses  show  the  earth  to  be  round ;  and  her  inequali- 
ties not  only  determine  the  form,  but  even  the  internal 
structure  of  our  planet ;  results  of  analysis  which  could 
not  have  been  anticipated.  Similar  inequalities  in  the 
motions  of  Jupiter's  satellites  prove  that  his  mass  is  not 
homogeneous,  and  that  his  compression  is  T^.?.  His 
equatorial  diameter  exceeds  his  polar  diameter  by  about 
6000  miles. 

The  phases  (N.  108)  of  the  moon,  which  vary  from 
a  slender  silvery  crescent  soon  after  conjunction  to  a 
complete  circular  disc  of  light  in  opposition,  decrease  by 
the  same  degrees  till  the  moon  is  again  enveloped  in 
the  morning  beams  of  the  sun.  These  changes  regulate 
the  returns  of  the  eclipses.  Those  .of  the  sun  can  only 
happen  in  conjunction,  when  the  moon,  coming  between 
the  earth  and  the  sun,  intercepts  his  light.  Those  of 


SECT.  V.  LUNAR  ECLIPSES.  39 

the  moon  are  occasioned  by  the  earth  intervening  be- 
tween the  sun  and  moon  when  in  opposition.  As  the 
earth  is  opaque  and  nearly  spherical,  it  throws  a  conical 
shadow  on  the  side  of  the  moon  opposite  to  the  sun,  the 
axis  of  which  passes  through  the  centers  of  the  sun  and 
earth  (N.  109).  The  length  of  the  shadow  terminates 
at  the  point  where  the  apparent  diameters  (N.  110) 
of  the  sun  and  earth  would  be  the  same.  When  the 
moon  is  in  opposition,  and  at  her  mean  distance,  the 
diameter  of  the  sun  would  be  seen  from  her  center 
under  an  angle  of  1918"-1.  That  of  the  earth  would 
appear  under  an  angle  of  6908"-3.  So  that  the  length 
of  the  shadow  is  at  least  three  times  and  a  half  greater 
than  the  distance  of  the  moon  from  the  earth,  and  the 
breadth  of  the  shadow,  where  it  is  traversed  by  the 
moon,  is  about  eight-thirds  of  the  lunar  diameter.  Hence 
the  moon  would  be  eclipsed  every  time  she  is  in  oppo- 
sition, were  it  not  for  the  inclination  of  her  orbit  to  the 
plane  of  the  ecliptic,  in  consequence  of  which  the  moon 
when  in  opposition  is  either  above  or  below  the  cone  of 
the  earth's  shadow,  except  when  in  or  near  her  nodes. 
Her  position  with  regard  to  them  occasions  all  the  vari- 
eties in  the  lunar  eclipses.  Every  point  of  the  moon's 
surface  successively  loses  the  light  of  different  parts  of 
the  sun's  disc  before  being  eclipsed.  Her  brightness 
therefore  gradually  diminishes  before  she  plunges  into 
the  earth's  shadow.  The  breadth  of  the  space  occupied 
by  the  penumbra  (N.  Ill)  is  equal  to  the  apparent  di- 
ameter of  the  sun,  as  seen  from  the  center  of  the  moon. 
The  mean  duration  of  a  revolution  of  the  sun,  with  re- 
gard to  the  node  of  the  lunar  orbit,  is  to  the  duration  of 
a  synodic  revolution  (N.  112)  of  the  moon  as  223  to  19. 
So  that,  after  a  period  of  223  lunar  months,  the  sun  and 
moon  would  return  to  the  same  relative  position  with 
regard  to  the  node  of  the  moon's  orbit,  and  therefore 
the  eclipses  would  recur  in  the  same  order,  were  not 
the  periods  altered  by  irregularities  in  the  motions  of 
the  sun  and  moon.  In  lunar  eclipses,  our  atmosphere 
bends  the  sun's  rays  which  pass  through  it  all  round 
into  the  cone  of  the  earth's  shadow.  And  as  the  hori- 
zontal refraction  (N.  113)  or  bending  of  the  rays  sur- 
passes half  the  sum  of  the  semidiameters  of  the  sun 


40  LUNAR  AND  SOLAR  ECLIPSES.  SECT.  V. 

and  moon,  divided  by  their  mutual  distance,  the  center 
of  the  lunar  disc,  supposed  to  be  in  the  axis  of  the 
shadow,  would  receive  the  rays  from  the  same  point  of 
the  sun,  round  all  sides  of  the  earth,  so  that  it  would  be 
more  illuminated  than  in  full  moon,  if  the  greater  por- 
tion of  the  light  were  not  stopped  or  absorbed  by  the 
atmosphere.  Instances  are  recorded  where  this  feeble 
light  has  been  entirely  absorbed,  so  that  the  moon  has 
altogether  disappeared  in  her  eclipses. 

The  sun  is  eclipsed  when  the  moon  intercepts  his 
rays  (N.  114).  The  moon,  though  incomparably  smaller 
than  the  sun,  is  so  much  nearer  the  earth,  that  her 
apparent  diameter  differs  but  little  from  his,  but  both 
are  liable  to  such  variations,  that  they  alternately  sur- 
pass one  another.  Were  the  eye  of  a  spectator  in  the 
same  straight  line  with  the  centers  of  the  sun  and  moon, 
he  would  see  the  sun  eclipsed.  If  the  apparent  diame- 
ter of  the  moon  surpassed  that  of  the  sun,  the  eclipse 
would  be  total.  If  it  were  less,  the  observer  would  see 
a  ring  of  light  round  the  disc  of  the  moon,  and  the 
eclipse  would  be  annular,  as  it  was  on  the  17th  of  May, 
1836.  If  the  center  of  the  moon  should  not  be  in  the 
straight  line  joining  the  centers  of  the  sun  and  the  eye 
of  the  observer,  the  moon  might  only  eclipse  a  part  of 
the  sun.  The  variation,  therefore,  in  the  distances  of 
the  sun  and  moon  from  the  center  of  the  earth,  and  of 
the  moon  from  her  node  at  the  instant  of  conjunction, 
occasions  great  varieties  in  the  solar  eclipses.  Besides, 
the  height  of  the  moon  above  the  horizon  changes  her 
apparent  diameter,  and  may  augment  or  diminish  the 
apparent  distances  of  the  centers  of  the  sun  and  moon, 
so  that  an  eclipse  of  the  sun  may  occur  to  the  inhabi- 
tants of  one  country,  and  not  to  those  of  another.  In 
this  respect  the  solar  eclipses  differ  from  the  lunar, 
which  are  the  same  for  every  part  of  the  earth  where 
the  moon  is  above  the  horizon.  In  solar  eclipses,  the 
light  reflected  by  the  atmosphere  diminishes  the  obscu- 
rity they  produce.  Even  in  total  eclipses  the  higher 
part  of  the  atmosphere  is  enlightened  by  a  part  of  the 
sun's  disc,  and  reflects  its  rays  to  the  earth.  The  whole 
disc  of  the  new  moon  is  frequently  visible  from  atmos- 
pheric reflection. 


S.CT.  V  ECLIPSES  OF  PLANETS.  41 

A  phenomenon  altogether  unprecedented  occurred 
during  the  total  eclipse  of  the  sun  which  happened  on 
the  8th  of  July,  1842.  The  moon  was  like  a  black 
patch  on  the  sky  surrounded  by  a  faint  whitish  light 
about  the  eighth  of  the  moon's  diameter  in  breadth,  in 
which  three  red  flames  appeared  in  form  like  the  teeth 
of  a  saw ;  from  what  cause  they  originated,  or  what 
they  were,  is  totally  unknown. 

Planets  sometimes  eclipse  one  another.  On  the  17th 
of  May,  1737,  Mercury  was  eclipsed  by  Venus  near 
their  inferior  conjunction ;  Mars  passed  over  Jupiter  on 
the  9th  of  January,  1591 ;  and  on  the  30th  of  October, 
1825,  the  moon  eclipsed  Saturn.  These  phenomena, 
however,  happen  very  seldom,  because  all  the  planets, 
or  even  a  part  of  them,  are  very  rarely  seen  in  con- 
junction at  once ;  that  is,  in  the  same  part  of  the  heav- 
ens at  the  same  time.  More  than  2500  years  before 
our  era,  the  five  great  planets  were  in  conjunction.  On 
the  15th  of  September,  1186,  a  similar  assemblage  took 
place  between  the  constellations  of  Virgo  and  Libra; 
and  in  1801,  the  moon,  Jupiter,  Saturn,  and  Venus 
were  united  in  the  heart  of  the  Lion.  These  conjunc- 
tions are  so  rare,  that  Lalande  has  computed  that  more 
than  seventeen  millions  of  millions  of  years  separate  the 
epochs  of  the  contemporaneous  conjunctions  of  the  six 
great  planets. 

The  motions  of  the  moon  have  now  become  of  more 
importance  to  the  navigator  and  geographer  than  those 
of  any  other  heavenly  body,  from  the  precision  with 
which  terrestrial  longitude  is  deter  mined  "by  occultations 
of  stars,  and  by  lunar  distances.  In  consequence  of  the 
retrograde  motion  of  the  nodes  of  the  lunar  orbit,  at  the 
rate  of  3'  10"-64  daily,  these  points  make  a  tour  of  the 
heavens  in  a  little  more  than  eighteen  years  and  a  half. 
This  causes  the  moon  to  move  round  the  earth  in  a  kind 
of  spiral,  so  that  her  disc  at  different  times  passes  over 
every  point  in  a  zone  of  the  heavens  extending  rather 
more  than  5°  9'  on  each  side  of  the  ecliptic.  It  is  there- 
fore evident,  that  at  one  time  or  other  she  must  eclipse 
every  star  and  planet  she  meets  with  in  this  space. 
Therefore  the  occultation  of  a  star  by  the  moon  is  a  phe- 
nomenon of  frequent  occurrence.  The  moon  seems  to 


42  DISTANCES,  HOW  FOUND.  SECT.  V. 

pass  over  the  star,  which  almost  instantaneously  vanishes 
at  one  side  of  her  disc,  and  after  a  short  time  as  suddenly 
reappears  on  the  other.  A  lunar  distance  is  the  ob- 
served distance  of  the  moon  from  the  sun,  or  from  a 
particular  star  or  planet,  at  any  instant.  The  lunar  the- 
ory is  brought  to  such  perfection,  that  the  times  of  these 
phenomena,  observed  under  any  meridian  when  com- 
pared with  those  computed  for  Greenwich  in  the  Nauti- 
cal Almanac,  give  the  longitude  of  the  observer  within  a 
few  miles  (N.  95). 

From  the  lunar  theory,  the  mean  distance  of  the  sun 
from  the  earth,  and  thence  the  whole  dimensions  of  the 
solar  system,  are  known.  For  the  forces  which  retain 
the  earth  and  moon  in  their  orbits  are  respectively  pro- 
portional to  the  radii  vectores  of  the  earth  and  moon, 
each  being  divided  by  the  square  of  its  periodic  time. 
And  as  the  lunar  theory  gives  the  ratio  of  the  forces, 
the  ratio  of  the  distances  of  the  sun  and  moon  from 
the  earth  is  obtained.  Hence  it  appears  that  the  sun's 
mean  distance  from  the  earth  is  396,  or  nearly  400 
times  greater  than  that  of  the  moon.  The  method  of 
finding  the  absolute  distances  of  the  celestial  bodies  in 
miles,  is  in  fact  the  same  with  that  employed  in  meas- 
uring the  distances  of  terrestrial  objects.  From  the 
extremities  of  a  known  base  (N.  115),  the  angles  which 
the  visual  rays  from  the  object  form  with  it,  are  meas- 
ured ;  their  sum  subtracted  from  two  right  angles  gives 
the  angle  opposite  the  base  ;  therefore,  by  trigonometry, 
all  the  angles  and  sides  of  the  triangle  may  be  computed 
— consequently  the  distance  of  the  object  is  found.  The 
angle  under  which  the  base  of  the  triangle  is  seen  from 
the  object  is  the  parallax  of  that  object.  It  evidently  in- 
creases and  decreases  with  the  distance.  Therefore  the 
base  must  be  very  great  indeed  to  be  visible  from  the 
celestial  bodies.  The  globe  itself,  whose  dimensions  are 
obtained  by  actual  admeasurement,  furnishes  a  standard 
of  measures,  with  which  we  compare  the  distances, 
masses,  densities,  and  volumes  of  the  sun  and  planets. 


SECT.  VI.      THEORETICAL  FORM  OF  THE  EARTH.  43 


SECTION  VI. 

Form  of  the  Earth  and  Planets— Figure  of  a  Homogeneous  Spheroid  in 
Rotation — Figure  of  a  Spheroid  of  Variable  Density — Figure  of  the 
Earth,  supposing  it  to  be  an  Ellipsoid  of  Revolution — Mensuration  of  a 
Degree  of  the  Meridian — Compression  and  Size  of  the  Earth  from 
Degrees  of  Meridian — Figure  of  Earth  from  the  Pendulum. 

THE  theoretical  investigation  of  the  figure  of  the  earth 
and  planets  is  so  complicated,  that  neither  the  geometry 
of  Newton,  nor  the  refined  analysis  of  La  Place,  has 
attained  more  than  an  approximation.  It  is  only  within 
a  few  years  that  a  complete  and  finite  solution  of  that 
difficult  problem  has  been  accomplished  by  our  distin- 
guished countryman  Mr.  Ivory.  The  investigation  has 
been  conducted  by  successive  steps,  beginning  with  a 
simple  case,  and  then  proceeding  to  the  more  difficult. 
But  in  all,  the  forces  which  occasion  the  revolutions  of 
the  earth  and  planets  are  omitted,  because,  by  acting 
equally  upon  all  the  particles,  they  do  not  disturb  their 
mutual  relations.  A  fluid  mass  of  uniform  density,  whose 
particles  mutually  gravitate  to  each  other,  will  assume 
the  form  of  a  sphere  when  at  rest.  But  if  the  sphere 
begins  to  revolve,  every  particle  will  describe  a  circle 
(N.  116),  having  its  center  in  the  axis  of  revolution. 
The  planes  of  all  these  circles  will  be  parallel  to  one 
another  and  perpendicular  to  the  axis,  and  the  particles 
will  have  a  tendency  to  fly  from  that  axis  in  consequence 
of  the  centrifugal  force  arising  from  the  velocity  of  rota- 
tion. The  force  of  gravity  is  everywhere  perpendicular 
to  the  surface  (N.  117),  and  tends  to  the  interior  of  the 
fluid  mass ;  whereas  the  centrifugal  force  acts  perpen- 
dicularly to  the  axis  of  rotation,  and  is  directed  to  the 
exterior.  And  as  its  intensity  diminishes  with  the  dis- 
tance from  the  axis  of  rotation,  it  decreases  from  the 
equator  to  the  poles,  where  it  ceases.  Now  it  is  clear 
that  these  two  forces  are  in  direct  opposition  to  each 
other  in  the  equator  alone,  and  that  gravity  is  there  di- 
minished by  the  whole  eflect  of  the  centrifugal  force, 
whereas,  in  every  other  part  of  the  fluid,  the  centrifugal 
force  is  resolved  into  two  parts,  one  of  which,  being  per- 
pendicular to  the  surface,  diminishes  the  force  of  grav- 


44  ROTATION  OF  A  FLUID  MASS.  SECT.  VI. 

ity ;  but  the  other,  being  at  a  tangent  to  the  surface, 
urges  the  particles  toward  the  equator,  where  they  ac- 
cumulate till  their  numbers  compensate  the  diminution 
of  gravity,  which  makes  the  mass  bulge  at  the  equator, 
and  become  flattened  at  the  poles.  It  appears,  then,  that 
the  influence  of  the  centrifugal  force  is  most  powerful  at 
the  equator,  not  only  because  it  is  actually  greater  there 
than  elsewhere,  but  because  its  whole  effect  is  employed 
in  diminishing  gravity,  whereas,  in  every  other  point  of 
the  fluid  mass,  it  is  only  a  part  that  is  so  employed.  For 
both  these  reasons,  it  gradually  decreases  toward  the 
poles,  where  it  ceases.  On  the  contraiy,  gravity  is  least 
at  the  equator,  because  the  particles  are  farther  from 
the  center  of  the  mass,  and  increases  toward  the  poles, 
where  it  is  greatest.  It  is  evident,  therefore,  that,  as 
the  centrifugal  force  is  much  less  than  the  force  of  grav- 
ity—  gravitation,  which  is  the  difference  between  the 
two,  is  least  at  the  equator,  and  continually  increases 
toward  the  poles,  where  it  is  a  maximum.  On  these 
principles  Sir  Isaac  Newton  proved  that  a  homogeneous 
fluid  (N.  118)  mass  in  rotation  assumes  the  form  of  an 
ellipsoid  of  revolution  (N.  119),  whose  compression  is 
-5— .  Such,  however,  cannot  be  the  form  of  the  earth, 
because  the  strata  increase  in  density  toward  the  center. 
The  lunar  inequalities  also  prove  the  earth  to  be  so  con- 
structed ;  it  was  requisite,  therefore,  to  consider  the  fluid 
mass  to  be  of  variable  density.  Including  this  condition, 
it  has  been  found  that  the  mass,  when  in  rotation,  would 
still  assume  the  form  of  an  ellipsoid  of  revolution  ;  that 
the  particles  of  equal  density  would  arrange  themselves 
in  concentric  elliptical  strata  (N.  120),  the  most  dense 
being  in  the  center;  but.  that  the  compression  or  flat- 
tening would  be  less  than  in  the  case  of  the  homogene- 
ous fluid.  The  compression  is  still  less  when  the  mass 
is  considered  to  be,  as  it  actually  is,  a  solid  nucleus,  de- 
creasing regularly  in  density  from  the  center  to  the  sur- 
face, and  partially  covered  by  the  ocean,  because  the 
solid  parts,  by  their  cohesion,  nearly  destroy  that  part 
of  the  centrifugal  force  which  gives  the  particles  a  ten- 
dency to  accumulate  at  the  equator,  though  not  alto- 
gether ;  otherwise  the  sea,  by  the  superior  mobility  of 
its  particles,  would  flow  toward  the  equator  and  leave 


S«CT.  VI.  FORM  OF  THE  EARTH.  45 

the  poles  dry.  Beside,  it  is  well  known,  that  the  con- 
tinents at  the  equator  are  more  elevated  than  they  are 
in  higher  latitudes.  It  is  also  necessary  for  the  equili- 
brium of  the  ocean,  that  its  density  should  be  less  than 
the  mean  density  of  the  earth,  otherwise  the  continents 
would  be  perpetually  liable  to  inundations  from  storms, 
and  other  causes.  On  the  whole,  it  appears  from  the- 
ory, that  a  horizontal  line  passing  round  the  earth 
through  both  poles,  must  be  nearly  an  ellipse,  having  its 
major  axis  in  the  plane  of  the  equator,  and  its  minor 
axis  coincident  with  the  axis  of  the  earth's  rotation 
(N.  121).  It  is  easy  to  show,  in  a  spheroid  whose 
strata  are  elliptical,  that  the  increase  in  the  length  of 
the  radii  (N.  122),  the  decrease  of  gravitation,  and  the 
increase  in  the  length  of  the  arcs  of  the  meridian,  cor- 
responding to  angles  of  one  degree,  from  the  poles  to 
the  equator,  are  all  proportional  to  the  square  of  the  co- 
sine of  the  latitude  (N.  123).  These  quantities  are  so 
connected  with  the  ellipticity  of  the  spheroid  that  the 
total  increase  in  the  length  of  the  radii  is  equal  to  the 
compression  or  flattening,  and  the  total  diminution  in  the 
length  of  the  arcs  is  equal  to  the  compression,  multi- 
plied by  three  times  the  length  of  an  arc  of  one  degree 
at  the  equator.  Hence,  by  measuring  the  meridian 
curvature  of  the  earth,  the  compression,  and  conse- 
quently its  figure,  become  known.  This,  indeed,  is  as- 
suming the  earth  to  be  an  ellipsoid  of  revolution,  but 
the  actual  measurement  of  the  globe  will  show  how  far 
it  corresponds  with  that  solid  in  figure  and  constitution. 

The  courses  of  the  great  rivers,  which  are  in  general 
navigable  to  a  considerable  extent,  prove  that  the  curva- 
ture of  the  land  differs  but  little  from  that  of  the  ocean ; 
and  as  the  heights  of  the  mountains  and  continents  are 
inconsiderable  when  compared  with  the  magnitude  of 
the  earth,  its  figure  is  understood  to  be  determined  by 
a  surface  at  every  point  perpendicular  to  the  direction 
of  gravitation,  or  of  the  plumb-line,  and  is  the  same 
which  the  sea  would  have,  if  it  were  continued  all  round 
the  earth  beneath  the  continents.  Such  is  the  figure 
that  has  been  measured  in  the  following  manner  : — 

A  terrestrial  meridian  is  a  line  passing  through  both 
poles,  all  the  points  of  which  have  their  noon  contem- 


46  ARCS  OF  THE  MERIDIAN.  SECT.  VI. 

poraneously.  Were  the  lengths  and  curvatures  of  dif- 
ferent meridians  known,  the  figure  of  the  earth  might 
be  determined.  But  the  length  of  one  degree  is  suffi- 
cient to  give  the  figure  of  the  earth,  if  it  be  measured 
on  different  meridians,  and  in  a  variety  of  latitudes.  For 
if  the  earth  were  a  sphere,  all  degrees  would  be  of  the 
same  length  ;  but  if  not,  the  lengths  of  the  degrees 
would  be  greater,  exactly  in  proportion  as  the  curvature 
is  less.  A  comparison  of  the  length  of  a  degree  in  dif- 
ferent parts  of  the  earth's  surface,  will  therefore  deter- 
mine its  size  and  form. 

An  arc  of  the  meridian  may  be  measured  by  observ- 
ing the  latitude  of  its  extreme  points  (N.  124),  and  then 
measuring  the  distance  between  them  in  feet  or  fath- 
oms. The  distance  thus  determined  on  the  surface  of 
the  earth,  divided  by  the  degrees  and  parts  of  a  degree 
contained  in  the  difference  of  the  latitudes,  will  give  the 
exact  length  of  one  degree,  the  difference  of  the  lati- 
tudes being  the  angle  contained  between  the  verticals 
at  the  extremities  of  the  arc.  This  would  be  easily  ac- 
complished were  the  distance  unobstructed,  and  on  a 
level  with  the  sea.  But,  on  account  of  the  innumerable 
obstacles  on  the  surface  of  the  earth,  it  is  necessary  to 
connect  the  extreme  points  of  the  arc  by  a  series  of  tri- 
angles (N.  125),  the  sides  and  angles  of  which  are  either 
measured  or  computed,  so  that  the  length  of  the  arc  is 
ascertained  with  much  laborious  calculation.  In  conse- 
quence of  the  irregularities  of  the  surface,  each  triangle 
is  in  a  different  plane.  They  must  therefore  be  reduced 
by  computation  to  what  they  would  have  been  had  they 
been  measured  on  the  surface  of  the  sea.  And  as  the 
earth  may  in  this  case  be  esteemed  spherical,  they  re- 
quire a  correction  to  reduce  them  to  spherical  triangles. 
The  gentlemen  who  conducted  the  trigonometrical  sur- 
vey, in  measuring  500  feet  of  a  base  in  Ireland  twice 
over,  found  that  the  difference  in  the  two  measurements 
did  not  amount  to  the  800th  part  of  an  inch.  Such  is 
the  accuracy  with  which  these  operations  are  conduct- 
ed, and  which  they  require. 

Arcs  of  the  meridian  have  been  measured  in  a  variety 
of  latitudes  north  and  south,  as  well  as  arcs  perpendicu- 
lar to  the  meridian.  From  these  measurements  it  ap- 


SECT.  VI.        FORM  OF  EARTH  FROM  PENDULUM.  47 

pears  that  the  length  of  the  degrees  increases  from  the 
equator  to  the  poles,  nearly  in  proportion  to  the  square 
of  the  sine  of  the  latitude  (N.  126).  Consequently,  the 
convexity  of  the  earth  diminishes  from  the  equator  to 
the  poles. 

Were  the  earth  an  ellipsoid  of  revolution,  the  merid- 
ians would  be  ellipses  whose  lesser  axes  would  coincide 
with  the  axis  of  rotation,  and  all  the  degrees  measured 
between  the  pole  and  the  equator  would  give  the  same 
compression  when  combined  two  and  two.  That,  how- 
ever, is  far  from  being  the  case.  Scarcely  any  of  the 
measurements  give  exactly  the  same  results,  chiefly  on 
account  of  local  attractions,  which  cause  the  plumb  line 
to  deviate  from  the  vertical.  The  vicinity  of  mountains 
has  that  effect.  But  one  of  the  most  remarkable,  though 
not  unprecedented,  anomalies  takes  place  in  the  plains  of 
the  north  of  Italy,  where  the  action  of  some  dense  sub- 
terraneous matter  causes  the  plumb-line  to  deviate  seven 
or  eight  times  more  than  it  did  from  the  attraction  of 
Chimborazo,  in  the  experiments  of  Bouguer,  while 
measuring  a  degree  of  the  meridian  at  the  equator.  In 
consequence  of  this  local  attraction,  the  degrees  of  the 
meridian  in  that  part  of  Italy  seem  to  increase  toward 
the  equator  through  a  small  space,  instead  of  decreasing, 
as  if  the  earth  was  drawn  out  at  the  poles,  instead  of 
being  flattened. 

Many  other  discrepancies  occur,  but  from  the  mean 
of  the  five  principal  measurements  of  arcs  in  Peru,  India, 
France,  England,  and  Lapland,  Mr.  Ivory  has  deduced 
that  the  figure  which  most  nearly  follows  this  law  is  an 
ellipsoid  of  revolution  whose  equatorial  radius  is  3962-824 
miles,  and  the  polar  radius  3949-585  miles.  The  differ- 
ence, or  13-239  miles,  divided  by  the  equatorial  radius, 
is  -i-g.  nearly.  This  fraction  is  called  the  compression 
of  the  earth,  and  does  not  differ  much  from  that  given 
by  the  lunar  inequalities.  If  we  assume  the  earth  to 
be  a  sphere,  the  length  of  a  degree  of  the  meridian  is 
69J^  British  miles.  Therefore  360  degrees,  or  the 
whole  circumference  of  the  globe,  is  24,856  miles,  and 
the  diameter,  which  is  something  less  than  a  third  of 
the  circumference,  is  about  7916,  or  8000  miles  nearly. 
Eratosthenes,  who  died  194  years  before  the  Christian 


48  FORM  OP  THE  EARTH.  SECT.  VI. 

era,  was  .the  first  to  give  an  approximate  value  ->f  the 
earth's  circumference,  by  the  measurement  of  an  arc 
between  Alexandria  and  Syene. 

There  is  another  method  of  finding  the  figure  of  the 
earth,  totally  different  from  the  preceding,  solely  depend- 
ing upon  the  increase  of  gravitation  from  the  equator  to 
the  poles.  The  force  of  gravitation  at  any  place  is 
measured  by  the  descent  of  a  heavy  body  during  the  first 
second  of  its  fall.  And  the  intensity  of  the  centrifugal 
force  is  measured  by  the  deflection  of  any  point  from  the 
tangent  in  a  second.  For,  since  the  centrifugal  force  bal- 
ances the  attraction  of  the  earth,  it  is  an  exact  measure  of 
the  gravitating  force.  Were  the  attraction  to  cease,  a  body 
on  the  surface  of  the  earth  would  fly  off  in  the  tangent 
by  the  centrifugal  force,  instead  of  bending  round  in  the 
circle  of  rotation.  Therefore,  the  deflection  of  the  cir- 
cle from  the  tangent  in  a  second  measures  the  intensity 
of  the  earth's  attraction,  and  is  equal  to  the  versed  sine 
of  the  arc  described  during  that  time,  a  quantity  easily 
determined  from  the  known  velocity  of  the  earth's  rota- 
tion. Whence  it  has  been  found,  that  at  the  equator 
the  centrifugal  force  is  equal  to  the  289th  part  of  gravity. 
Now,  it  is  proved  by  analysis  that  whatever  the  consti- 
tution of  the  earth  and  planets  may  be,  if  the  intensity 
of  gravitation  at  the  equator  be  taken  equal  to  unity,  the 
sum  of  the  compression  of^the  ellipsoid,  and  the  whole 
increase  of  gravitation  from  the  equator  to  the  pole,  is 
equal  to  five  halves  of  the  ratio  of  the  centrifugal  force 
to  gravitation  at  the  equator.  This  quantity  with  regard 
to  the  earth  is  4  of  -^?,  or  tiT-^-  Consequently,  the 
compression  of  the  earth  is  equal  to  y-fj.-o  diminished  by 
the  whole  increase  of  gravitation.  So  that  its  form  will 
be  known,  if  the  whole  increase  of  gravitation  from  the 
equator  to  the  pole  can  be  determined  by  experiment. 
This  has  been  accomplished  by  a  method  founded  upon 
the  following  considerations  : — If  the  earth  were  a  homo- 
geneous sphere  without  rotation,  its  attraction  on  bodies 
at  its  surface  would  be  everywhere  the  same.  If  it 
be  elliptical  and  of  variable  density,  the  force  of  gravity, 
theoretically,  ought  to  increase  from  the  equator  to  the 
pole,  as  unity  plus  a  constant  quantity  multiplied  into  the 
square  of  the  sine  of  the  latitude  (N.  126).  But  for  a 


SKCT.  VI.  OSCILLATIONS  OF  PENDULUM.      .  49 

spheroid  in  rotation,  the  centrifugal  force  varies,  by  the 
i\vs  of  mechanics,  as  the  square  of  the  sine  of  the  lati- 
tude, from  the  equator,  where  it  is  greatest,  to  the  pole, 
where  it  vanishes.  And  as  it  tends  to  make  bodies  fly 
off  the  surface,  it  diminishes  the  force  of  gravity  by  a 
small  quantity.  Hence,  by  gravitation,  which  is  the  dif- 
ference of  these  two  forces,  the  fall  of  bodies  ought  to 
be  accelerated  from  the  equator  to  the  poles  proportion- 
ably  to  the  square  of  the  sine  of  the  latitude ;  and  the 
weight  of  the  same  body  ought  to  increase  in  that  ratio. 
This  is  directly  proved  by  the  oscillations  of  the  pendu- 
lum (N.  127),  which,  in  fact,  is  a  falling  body;  for  if  the 
faH  of  bodies  be  accelerated,  the  oscillations  will  be  more 
rapid  :  in  order,  therefore,  that  they  may  always  be  per- 
formed in  the  same  time,  the  length  of  the  pendulum 
must  be  altered.  By  numerous  and  careful  experi- 
ments, it  is  proved  that  a  pendulum  which  oscillates 
86,400  times  in  a  mean  day  at  the  equator,  will  do  the 
same  at  every  point  of  the  earth's  surface,  if  its  length 
be  increased  progressively  to  the  pole,  as  the  square  of 
the  sine  of  the  latitude. 

From  the  mean  of  these  it  appears  that  the  whole 
decrease  of  gravitation  from  the  poles  to  the  equator  is 
0-005.1449,  which,  subtracted  from  -j-f^.o'  shows  that 
the  compression  of  the  terrestrial  spheroid  is  about 
_|^  _7.  This  value  has  been  deduced  by  the  late  Mr. 
Bally,  president  of  the  Astronomical  Society,  who  has 
devoted  much  attention  to  this  subject ;  at  the  same 
time,  it  may  be  observed  that  no  two  sets  of  pendulum 
experiments  give  the  same  result,  probably  from  local 
attractions.  Therefore,  the  question  cannot  be  con- 
sidered as  definitively  settled,  though  the  differences 
are  very  small.  The  compression  obtained  by  this 
method  does  not  differ  much  from  that  given  by  the 
lunar  inequalities,  nor  from  the  arcs  in  the  direction  of 
the  meridian,  and  those  perpendicular  to  it.  The  near 
coincidence  of  these  three  values,  deduced  by  methods 
so  entirely  independent  of  each  other,  shows  that  the 
mutual  tendencies  of  the  centers  of  the  celestial  bodies 
to  one  another  and  the  attraction  of  the  earth  for  bodies 
at  its  surface  result  from  the  reciprocal  attraction  of  all 
their  particles.  Another  proof  may  be  added.  The 
4  K 


50  COMPRESSION  OF  THE  EARTH.  SECT.  VI 

nutation  of  the  earth's  axis  and  the  precession  of  the 
equinoxes  (N.  143)  are  occasioned  by  the  action  of  the 
sun  and  moon  on  the  protuberant  matter  at  the  earth's 
equator.  And  although  these  inequalities  do  not  give 
the  absolute  value  of  the  terrestrial  compression,  they 
show  that  the  fraction  expressing  it  is  comprised  be- 
tween the  limits  T^-  and  ^|¥. 

It  might  be  e'xpected  that  the  same  compression 
should  result  from  each,  if  the  different  methods  of  ob- 
servation could  be  made  without  error.  This,  however, 
is  not  the  case  ;  for,  after  allowance  has  been  made  for 
every  cause  of  error,  such  discrepancies  are  found,  both 
in  the  degrees  of  the  meridian  and  in  the  length  of  the 
pendulum,  as  show  that  the  figure  of  the  earth  is  very 
complicated.  But  they  are  so  small,  when  compared 
with  the  general  results,  that  they  may  be  disregarded. 
The  compression  deduced  from  the  mean  of  the  whole 
appears  not  to  differ  much  from  ¥*T  ;  that  given  by  the 
lunar  theory  has  the  advantage  of  being  independent  of 
the  irregularities  of  the  earth's  surface  and  of  local  at- 
tractions. The  regularity  with  which  the  observed 
variation  in  the  length  of  the  pendulum  follows  the  law 
of  the  square  of  the  sine  of  the  latitude,  proves  the 
strata  to  be  elliptical,  and  symmetrically  disposed  round 
the  center  of  gravity  of  the  earth,  which  affords  a  strong 
presumption  in  favor  of  its  original  fluidity.  It  is  re- 
markable how  little  influence  the  sea  has  on  the  varia- 
tion of  the  lengths  of  the  arcs  of  the  meridian,  or  on 
gravitation ;  neither  does  it  much  affect  the  lunar  ine- 
qualities, from  its  density  being  only  about  a  fifth  of  the 
mean  density  of  the  earth.  For,  if  the  earth  were  to 
become  a  fluid,  after  being  stripped  of  the  ocean,  it 
would  assume  the  form  of  an  ellipsoid  of  revolution 
whose  compression  is  ^|?.7,  which  differs  very  little 
from  that  determined  by  observation,  and  proves,  not 
only  that  the  density  of  the  ocean  is  inconsiderable,  but 
that  its  mean  depth  is  very  small.  There  may  be  pro- 
found cavities  in  the  bottom  of  the  sea,  but  its  mean 
depth  probably  does  not  much  exceed  the  mean  height 
of  the  continents  and  islands  above  its  level.  On  this 
account,  immense  tracts  of  land  may  be  deserted  or 
overwhelmed  by  the  ocean,  as  appears  really  to  have 


S«CT.  VII.  PARALLAX.  51 

been  the  case,  without  any  great  change  in  the  form  of 
the  terrestrial  spheroid.  The  variation  in  the  length  of 
the  pendulum  was  first  remarked  by  Richter  in  1672, 
while  observing  transits  of  the  fixed  stars  across  the 
meridian  at  Cayenne,  about  five  degrees  north  of  the 
equator.  He  found  that  his  clock  lost  at  the  rate  of 
2m  28s  daily,  which  induced  him  TO  determine  the 
length  of  a  pendulum  beating  seconds  in  that  latitude ; 
and  repeating  the  experiments  on  his  return  to  Europe, 
he  found  the  seconds'  pendulum  at  Paris  to  be  more 
than  the  twelfth  of  an  inch  longer  than  that  at  Cayenne. 
The  form  and  size  of  the  earth  being  determined, 
a  standard  of  measure  is  furnished  with  which  the  di- 
mensions of  the  solar  system  may  be  compared. 


SECTION  VII. 

Parallax — Lunar  Parallax  found  from  direct  Observation — Solar  Parallax 
deduced  from  the  Transit  of  Venus — Distance  of  the  Sun  from  the 
Earth— Annual  Parallax— Distance  of  the  Fixed  Stars. 

THE  parallax  of  a  celestial  body  is  the  angle  under 
which  the  radius  of  the  earth  would  be  seen,  if  viewed 
from  the  center  of  that  body ;  it  affords  the  means  of 
ascertaining  the  distances  of  the  sun,  moon,  and  planets 
(N.  128).  When  the  moon  is  in  the  horizon  at  the 
instant  of  rising  or  setting,  suppose  lines  to  be  drawn 
from  her  center  to  the  spectator  and  to  the  center  of  the 
earth ;  these  would  form  a  right-angled  triangle  with 
the  terrestrial  radius,  which  is  of  a  known  length ;  and 
as  the  parallax  or  angle  at  the  moon  can  be  measured, 
ah"  the  angles  and  one  side  are  given ;  whence  the 
distance  of  the  moon  from  the  center  of  the  earth  may 
be  computed.  The  parallax  of  an  object  may  be  found, 
if  two  observers  under  the  same  meridian,  but  at  a  very 
great  distance  from  one  another,  observe  its  zenith 
distances  on  the  same  day  at  the  time  of  its  passage 
over  the  meridian.  By  such  contemporaneous  obser- 
vations at  the  Cape  of  Good  Hope  and  at  Berlin,  the 
mean  horizontal  parallax  of  the  moon  was  found  to  be 
3459",  whence  the  mean  distance  of  the  moon  is  about 
sixty  times  the  mean  terrestrial  radius,  or  237,360  miles 


52  TRANSIT  OF  VENUS.  SECT.  VII 

nearly.  Since  the  parallax  is  equal  to  the  radius  of  the 
earth  divided  by  the  distance  of  the  moon,  it  varies  with 
the  distance  of  the  moon  from  the  earth  under  the 
same  parallel  of  latitude,  and  proves  the  ellipticity  of  the 
lunar  orbit.  When  the  moon  is  at  her  mean  distance, 
it  varies  with  the  terrestrial  radii,  thus  showing  that 
the  earth  is  not  a  sphere  (N.  129). 

Although  the  method  described  is  sufficiently  accurate 
for  finding  the  parallax  of  an  object  as  near  as  the  moon, 
it  will  not  answer  for  the  sun,  which  is  so  remote  that 
the  smallest  error  in  observation  would  lead  to  a  false 
result.  But  that  difficulty  is  obviated  by  the  transits  of 
Venus.  When  that  planet  is  in  her  nodes  (N.  130),  or 
within  1|°  of  them,  that  is,  in,  or  nearly  in,  the  plane 
of  the  ecliptic,  she  is  occasionally  seen  to  pass  over  the 
sun  like  a  black  spot.  If  we  could  imagine  that  the  sun 
and  Venus  had  no  parallax,  the  line  described  by  the 
planet  on  his  disc,  and  the  duration  of  the  transit,  would 
be  the  same  to  all  the  inhabitants  of  the  earth.  But  as 
the  semi-diameter  of  the  earth  has  a  sensible  magnitude 
when  viewed  from  the  center  of  the  sun.  the  line  de- 
scribed by  the  planet  in  its  passage  over  his  disc  appears 
to  be  nearer  to  his  center,  or  farther  from  it,  according 
to  the  position  of  the  observer ;  so  that  the  duration  of 
the  transit  varies  with  the  different  points  of  the  earth's 
surface  at  which  it  is  observed  (N.  131).  This  differ- 
ence of  time,  being  entirely  the  effect  of  parallax,  fur- 
nishes the  means  of  computing  it  from  the  known 
motions  of  the  earth  and  Venus,  by  the  same  method  as 
for  the  eclipses  of  the  sun.  In  fact,  the  ratio  of  the 
distances  of  Venus  and  the  sun  from  the  earth  at  the 
time  of  the  transit  are  known  from  the  theory  of  their 
elliptical  motion.  Consequently  the  ratio  of  the  paral- 
laxes of  these  two  bodies  being  inversely  as  their  dis- 
tances, is  given  ;  and  as  the  transit  gives  the  difference  of 
the  parallaxes,  that  of  the  sun  is  obtained.  In  1769.  the 
parallax  of  the  sun  was  determined  by  observations  of  a 
transit  of  Venus  made  at  Wardhus  in  Lapland,  and  at 
Otaheite  in  the  South  Sea.  The  latter  observation  was 
the  object  of  Cook's  first  voyage.  The  transit  lasted 
about  six  hours  at  Otaheite,  and  the  difference  in  dura- 
tion at  these  two  stations  was  eight  minutes ;  whence 


SKCT.  VII.  SOLAR  PARALLAX.  53 

the  sun's  horizontal  parallax  was  found  to  be  8"-72. 
But  by  other  considerations  it  has  been  reduced  by 
Professor  Encke  to  8"-5776 ;  from  which  the  mean 
distance  of  the  sun  appears  to  be  about  ninety-five  mil- 
lions of  miles.  This  is  confirmed  by  an  inequality  in  the 
motion  of  the  moon,  which  depends  upon  the  parallax  of 
the  sun,  and  which,  when  compared  with  observation, 
gives  8"- 6  for  the  sun's  parallax. 

The  parallax  of  Venus  is  determined  by  her  transits ; 
that  of  Mars  by  direct  observation,  and  it  is  found  to  be 
nearly  double  that  of  the  sun,  when  the  planet  is  in 
opposition.  The  distance  of  these  two  planets  from 
the  earth  is  therefore  known  in  terrestrial  radii,  conse- 
quently their  mean  distances  from  the  sun  may  be 
computed  ;  and  as  the  ratios  of  the  distances  of  the 
planets  from  the  sun  are  known  by  Kepler's  law,  of  the 
squares  of  the  periodic  times  of  any  two  planets  being 
as  the  cubes  of  their  mean  distances  from  the  sun,  their 
absolute  distances  in  miles  are  easily  found  (N.  132). 
This  law  is  very  remarkable,  in  thus  uniting  all  the 
bodies  of  the  system,  and  extending  to  the  satellites  as 
well  as  the  planets. 

Far  as  the  earth  seems  to  be  from  the  sun,  Uranus  is 
no  less  than  nineteen  times  farther.  Situate  on  the 
verge  of  the  system,  the  sun  must  appear  to  it  not 
much  larger  than  Venus  does  to  us.  The  earth  cannot 
even  be  visible  as  a  telescopic  object  to  a  body  so  re- 
mote. Yet  man,  the  inhabitant  of  the  earth,  soars 
beyond  the  vast  dimensions  of  the  system  to  which  his 
planet  belongs,  and  assumes  the  diameter  of  its  orbit 
as  the  base  of  a  triangle  whose  apex  extends  to  the 
stars. 

Sublime  as  the  idea  is,  this  assumption  proves  in- 
effectual, except  in  a  very  few  cases ;  for  the  apparent 
places  of  the  fixed  stars  are  not  sensibly  changed  by  the 
earth's  annual  revolution.  With  the  aid  derived  from 
the  refinements  of  modern  astronomy,  and  of  the  most 
perfect  instruments,  a  sensible  parallax  has  been  de- 
tected only  in  a  veiy  few  of  these  remote  suns,  a  Cen- 
tauri  has  a  parallax  of  one  second  of  space,  therefore  it 
is  the  nearest  known  star,  and  yet  it  is  more  than  two 
hundred  thousand  times  farther  from  us  fhan  the  sun 

K2 


54  MASSES  OF  THE  PLANETS.  SECT.  VHI. 

is.  At  such  a  distance  not  only  the  terrestrial  orbit 
shrinks  to  a  point,  but  the  whole  solar  system,  seen  in 
the  focus  of  the  most  powerful  telescope,  might  be 
eclipsed  by  the  thickness  of  a  spider's  thread.  Light, 
flying  at  the  rate  of  190,000  miles  in  a  second,  would 
take  more  than  three  years  to  travel  over  that  space. 
One  of  the  nearest  stars  may  therefore  have  been 
kindled  or  extinguished  more  than  three  years,  before 
we  could  have  been  aware  of  so  mighty  an  event.  But 
this  distance  must  be  small,  when  compared  with  that 
of  the  most  remote  of  the  bodies  which  are  visible  in 
the  heavens.  The  fixed  stars  are  undoubtedly  luminous 
like  the  sun ;  it  is  therefore  probable  that  they  are  not 
nearer  to  one  another  than  the  sun  is  to  the  nearest  of 
them.  In  the  milky  way  and  the  other  stariy  nebulae, 
some  of  the  stars  that  seem  to  us  to  be  close  to  others, 
may  be  far  behind  them  in  the  boundless  depths  of 
space;  nay,  may  be  rationally  supposed  to  be  situate 
many  thousand  times  farther  off.  Light  would  there- 
fore require  thousands  of  years  to  come  to  the  earth 
from  those  myriads  of  suns  of  which  our  own  is  but 
"the  remote  companion." 


SECTION  VIII. 

Masses  of  Planets  that  have  no  Satellites  determined  from  their  Perturba- 
tions— Masses  of  the  others  obtained  from  the  Motions  of  their  Satellites 
—Masses  of  the  Sun,  the  Earth,  of  Jupiter,  and  of  the  Jovial  System- 
Mass  of  the  Moon— Real  Diameters  of  Planets,  how  obtained— Size  of 
Sun — Densities  of  the  Heavenly  Bodies — Formation  of  Astronomical 
Tables — Requisite  Data  and  Means  of  obtaining-  them. 

THE  masses  of  such  planets  as  have  no  satellites,  are 
known  by  comparing  the  inequalities  they  produce  in 
the  motions  of  the  earth  and  of  each  other,  determined 
theoretically,  with  the  same  inequalities  given  by  ob- 
servation;  for  the  disturbing  cause  must  necessarily 
be  proportional  to  the  effect  it  produces.  The  masses 
of  the  satellites  themselves  may  also  be  compared  with 
that  of  the  sun  by  their  perturbations.  Thus,  it  is 
found,  from  the  comparison  of  a  vast  number  of  observa- 
tions, with  La  Place's  theory  of  Jupiter's  satellites, 


VIII.  MASS  OP  THE  MOON.  55 

that  the  mass  of  the  sun  is  no  less  than  65,000,000 
times  greater  than  the  least  of  these  moons.  But  as 
the  quantities  of  matter  in  any  two  primary  planets  are 
directly  as  the  cubes  of  the  mean  distances  at  which 
their  satellites  revolve,  and  inversely  as  the  squares  of 
their  periodic  times  (N.  133),  the  mass  of  the  sun  and 
of  any  planets  which  have  satellites  may  be  compared 
with  the  mass  of  the  earth.  In  this  manner  it  is  com- 
puted that  the  mass  of  the  sun  is  354,936  times  that 
of  the  earth ;  whence  the  great  perturbations  of  the 
moon,  and  the  rapid  motion  of  the  perigee  and  nodes  of 
her  orbit  (N.  134).  Even  Jupiter,  the  largest  of  the 
planets,  has  recently  been  found  by  Professor  Airy  to 
be  1048-7  times  less  than  the  sun;  and,  indeed,  the 
mass  of  the  whole  Jovial  System  is  not  more  than  the 
1046-77th  part  of  that  of  the  sun.  So  that  the  mass  of 
the  satellites  bears  a  very  small  proportion  to  that  of 
their  primary.  The  mass  of  the  moon  is  determined 
from  several  sources — from  her  action  on  the  terres- 
trial equator,  which  occasions  the  nutation  in  the  axis  of 
rotation;  from  her  horizontal  parallax;  from  an  in- 
equality she  produces  in  the  sun's  longitude ;  and  from 
her  action  on  the  tides.  The  three  first  quantities, 
computed  from  theory  and  compared  with  their  ob- 
served values,  give  her  mass  respectively  equal  to  the 
T»_t  ?|.-,  and,  -^.o-  part  of  that  of  the  earth,  which  do 
not  differ  much  from  each  other.  Dr.  Brinkley,  Bishop 
of  Cloyne,  has  found  it  to  be  ^  from  the  constant  of 
lunar  nutation;  but  from  the  moon's  action  in  raising 
the  tides,  her  mass  appears  to  be  about  the  Jj  part  of 
that  of  the  earth — a  value  that  cannot  differ  much  from 
the  truth. 

The  apparent  diameters  of  the  sun,  moon,  and  planets 
are  determined  by  measurement ;  therefore,  their  real 
diameters  may  be  compared  with  that  of  the  earth ;  for 
the  real  diameter  of  a  planet  is  to  the  real  diameter  of 
the  earth,  or  7916  miles,  as  the  apparent  diameter  of 
the  planet  to  the  apparent  diameter  of  the  earth  as  seen 
from  the  planet,  that  is,  to  twice  the  parallax  of  the 
planet.  According  to  Professor  Bessel,  the  mean  ap- 
parent diameter  of  the  sun  is  1922",  and  with  the  solar 
parallax  8"-5776,  it  will  be  found  thatHhe  diameter  of 


56  DENSITIES  OF  CELESTIAL  BODIES.     SECT.  VIII. 

the  sun  is  about  886,877  miles.  Therefore,  if  the  cen- 
ter of  the  sUn  were  to  coincide  with  the  center  of  the 
earth,  his  volume  would  not  only  include  the  orbit  of 
the  moon,  but  would  extend  nearly  as  far  again ;  for 
the  moon's  mean  distance  from  the  earth  is  about  sixty 
times  the  earth's  mean  radius,  or  237,360  miles  :  so  that 
twice  the  distance  of  the  moon  is  474,720  miles,  which 
differs  but  little  from  the  solar  radius ;  his  equatorial 
radius  is  probably  not  much  less  than  the  major  axis  of 
the  lunar  orbit.  The  diameter  of  the  moon  is  only  2160 
miles  ;  and  Jupiter's  diameter  of  87,000  miles  is  very 
much  less  than  that  of  the  sun ;  the  diameter  of  Pallas 
does  not  much  exceed  79  miles,  so  that  an  inhabitant  of 
that  planet,  in  one  of  our  steam  carriages,  might  go 
round  his  world  in  a  few  hours. 

The  densities  of  bodies  are  proportional  to  their 
masses,  divided  by  their  volumes.  Hence,  if  the  sun 
and  planets  be  assumed  to  be  spheres,  their  volumes 
will  be  as  the  cubes  of  their  diameters.  Now,  the  ap- 
parent diameters  of  the  sun  and  earth,  at  their  mean 
distance,  are  1922"  and  17//<1552,  and  the  mass  of  the 
earth  is  the  354,936th  part  of  that  of  the  sun  taken  as 
the  unit.  It  follows,  therefore,  that  the  earth  is  nearly 
four  times  as  dense  as  the  sun.  But  the  sun  is  so  large, 
that  his  attractive  force  would  cause  bodies  to  fall 
through  about  334-65  feet  in  a  second.  Consequently, 
if  he  were  habitable  by  human  beings,  they  would  be 
unable  to  move,  since  their  weight  would  be  thirty  times 
as  great  as  it  is  here.  A  man  of  moderate  size  would 
weigh  about  two  tons  at  the  surface  of  the  sun ;  where- 
as at  the  surface  of  the  four  new  planets  he  would  be  so 
light,  that  it  would  be  impossible  to  stand  steady,  since 
he  would  only  weigh  a  few  pounds.  The  mean  density 
of  the  earth  has  been  recently  determined  with  a  de- 
gree of  accuracy  that  leaves  nothing  farther  to  be  de- 
sired. Since  a  comparison  of  the  action  of  two  planets 
upon  a  third  gives  the  ratio  of  the  masses  of  these  two 
planets,  it  is  clear  that  if  we  can  compare  the  effect  of 
the  whole  earth  with  the  effect  of  any  part  of  it,  a  com- 
parison may  be  instituted  between  the  mass  of  the 
whole  earth  and  the  mass  of  that  part  of  it.  Now  a 
leaden  ball  was  weighed  against  the  earth  by  comparing 


SECT.  VIII.  ASTRONOMICAL  TABLES.  57 

the  effects  of  each  upon  a  pendulum ;  the  nearness  of 
the  smaller  mass  making  it  produce  a  sensible  effect  as 
compared  with  that  of  the  larger :  for  by  the  laws  of 
attraction  the  whole  earth  must  be  considered  as  col- 
lected in  its  center.  By  this  method  it  has  been  found 
that  the  mean  density  -of  the  earth  is  5-675  times  greater 
than  that  of  water  at  the  temperature  of  62°  of  Fahren- 
heit's thermometer.  The  late  Mr.  Baily,  whose  accu- 
racy as  an  experimental  philosopher  is  acknowledged, 
was  unremittingly  occupied  nearly  four  years  in  accom- 
plishing this  very  important  object.  All  the  planets  and 
satellites  appear  to  be  of  less  density  fhan  the  earth. 
The  motion  of  Jupiter's  satellites  show  that  his  density 
increases  toward  his  center.  Were  his  mass  homogene- 
ous, his  equatorial  and  polar  axis  would  be  in  the  ratio 
of  41  to  36,  whereas  they  are  observed  to  be  only  as  41 
to  38.  The  singular  irregularities  in  the  form  of  Sat- 
urn, and  the  great  compression  of  Mars,  prove  the  in- 
ternal structure  of  these  two  planets  to  be  very  far  from 
uniform. 

Before  entering  on  the  theory  of  rotation,  it  may  not 
be  foreign  to  the  subject  to  give  some  idea  of  the  meth- 
ods of  computing  the  places  of  the  planets,  and  of  form- 
ing astronomical  tables.  Astronomy  is  now  divided  into 
the  three  distinct  departments  of  theory,  observation, 
and  computation.  Since  the  problem  of  the  three  bod- 
ies can  only  be  solved  by  approximation,  the  analytical 
astronomer  determines  the  position  of  a  planet  in  space 
by  a  series  of  corrections.  Its  place  in  its  circular  orbit 
is  first  found,  then  the  addition  or  subtraction  of  the 
equation  of  the  center  (N.  48)  to  or  from  its  mean  place, 
gives  its  position  in  the  ellipse.  This  again  is  corrected 
by  the  application  of  the  principal  periodic  inequalities. 
But  as  these  are  determined  for  some  particular  position 
of  the  three  bodies,  they  require  to  be  corrected  to  suit 
other  relative  positions.  This  process  is  continued  till 
the  corrections  become  less  than  the  errors  of  observa- 
tion, when  it  is  obviously  unnecessary  to  carry  the  ap- 
proximation further.  The  true  latitude  and  distance  of 
the  planet  from  the  sun  are  obtained  by  methods  similar 
to  those  employed  for  the  longitude. 

As  the  earth  revolves  equably  about  its  axis  in  24 


58  ASTRONOMICAL  TABLES.  SECT.  VIII. 

hours,  at  the  rate  of  15°  in  an  hour,  time  becomes  a 
measure  of  angular  motion  and  the  principal  element  in 
astronomy,  where  the  object  is  to  determine  the  exact 
state  of  the  heavens,  and  the  successive  changes  it  under- 
goes in  all  ages,  past,  present,  and  to  come.  Now  the 
longitude,  latitude,  and  distance  of  a  planet  from  the 
sun,  are  given  in  terms  of  the  time,  by  general  analytical 
formulae.  These  formulae  will  consequently  give  the 
exact  place  of  the  body  in  the  heavens,  for  any  time  as- 
sumed at  pleasure,  provided  they  can  be  reduced  to 
numbers.  But  before  the  calculator  begins  his  task,  the 
observer  must  furnish  the  necessaiy  data,  which  are, 
obviously,  the  forms  of  the  orbits,  and  their  positions 
with  regard  Jo  the  plane  of  the  ecliptic  (N.  57).  It  is 
therefore  necessary  to  determine  by  observation  for  each 
planet,  the  length  of  the  major  axis  of  its  orbit,  the  ec- 
centricity, the  inclination  of  the  orbit  to  the  plane  of  the 
ecliptic,  the  longitudes  of  its  perihelion  and  ascending 
node  at  a  given  time,  the  periodic  time  of  the  planet, 
and  its  longitude  at  any  instant  arbitrarily  assumed,  as 
an  origin  from  whence  all  its  subsequent  and  antecedent 
longitudes  are  estimated.  Each  of  these  quantities  is 
determined  from  that  position  of  the  planet  on  which  it 
has  most  influence.  For  example,  the  sum  of  the  great- 
est and  least  distances  of  the  planet  from  the  sun  is 
equal  to  the  major  axis  of  the  orbit,  and  their  difference 
is  equal  to  twice  the  eccentricity.  The  longitude  of  the 
planet,  when  at  its  least  distance  from  the  sun,  is  the 
same  with  the  longitude  of  the  perihelion  ;  the  greatest 
latitude  of  the  planet  is  equal  to  the  inclination  of  the 
orbit ;  the  longitude  of  the  planet,  when  in  the  plane  of 
the  ecliptic  in  passing  toward  the  north,  is  the  longitude 
of  the  ascending  node,  and  the  periodic  time  is  the  in- 
terval between  two  consecutive  passages  of  the  planet 
through  the  same  node,  a  small  correction  being  made 
for  the  precession  of  the  node,  during  the  revolution  of 
the  planet  (N.  135).  Notwithstanding  the  excellence  of 
instruments  and  the  accuracy  of  modern  observers,  una- 
voidable errors  of  observation  can  only  be  compensated 
by  finding  the  value  of  each  element  from  the  mean  of 
a  thousand,  or  even  many  thousands  of  observations. 
For  as  it  is  probable  that  the  errors  are  not  all  in  one 


S«cr.  VHI.  CORRECTION  OF  ELEMENTS.  59 

direction,  but  that  some  are  in  excess  and  others  in  de- 
fect, they  will  compensate  each  other  when  combined. 

However,  the  values  of  the  elements  determined  sep- 
arately, can  only  be  regarded  as  approximate,  because 
they  are  so  connected,  that  the  estimation  of  any  one 
independently,  will  induce  errors  in  the  others.  The 
eccentricity  depends  upon  the  longitude  of  the  perihe- 
lion, the  mean  motion  depends  upon  the  major  axis,  the 
longitude  of  the  node  upon  the  inclination  of  the  orbit, 
and  vice  versa.  Consequently,  the  place  of  a  planet  com- 
puted with  the  approximate  data  will  differ  from  its  ob- 
served place.  Then  the  difficulty  is  to  ascertain  what 
elements  are  most  in  fault,  since  the  difference  in  ques- 
tion is  the  error  of  all ;  that  is  obviated  by  finding  the 
errors  of  some  thousands  of  observations,  and  combining 
them,  so  as  to  correct  the  elements  simultaneously,  and 
to  make  the  sum  of  the  squares  of  the  errors  a  minimum 
with  regard  to  each  element  (N.  136).  The  method  of 
accomplishing  this  depends  upon  the  Theory  of  Proba- 
bilities ;  a  subject  fertile  in  most  important  results  in  the 
various  departments  of  science  and  of  civil  life,  and  quite 
indispensable  in  the  determination  of  astronomical  data. 
A  series  of  observations  continued  for  some  years  will 
give  approximate  values  of  the  secular  and  periodic  ine- 
qualities, which  must  be  corrected  from  time  to  time, 
till  theory  and  observation  agree.  And  these  again  will 
give  values  of  the  masses  of  the  bodies  forming  the  solar 
system,  which  are  important  data  in  computing  their 
motions.  The  periodic  inequalities  derived  from  a  great 
number  of  observations  are  employed  for  the  determina- 
tion of  the  values  of  the  masses  till  such  time  as  the 
secular  inequalities  shall  be  perfectly  known,  which  will 
then  give  them  with  all  the  necessary  precision.  When 
all  these  quantities  are  determined  in  numbers,  the  lon- 
gitude, latitude,  and  distance  of  the  planet  from  the 
sun  are  computed  for  stated  intervals,  and  formed  into 
tables,  arranged  according  to  the  time  estimated  from  a 
given  epoch,  so  that  the  place  of  the  body  may  be  deter- 
mined from  them  by  inspection  alone,  at  any  instant,  for 
perhaps  a  thousand  years  before  and  after  that  epoch. 
By  this  tedious  process,  tables  have  been  computed  for 
eleven  planets,  besides  the  moon  and  the  satellites  of 


60  ASTRONOMICAL  TABLES.  SKCT.  IX 

Jupiter.  In  the  present  state  of  astronomy,  the  masses 
and  elements  of  the  orbits  are  pretty  well  known^  so 
that  the  tables  only  require  to  be  corrected  from  time 
to  time,  as  observations  become  more  accurate.  Those 
containing  the  motions  of  Jupiter,  Saturn,  and  Uranus, 
have  already  been  twice  constructed  within  the  last  thirty 
years.  The  tables  of  Jupiter  and  Saturn  agree  almost 
perfectly  with  modern  observation  ;  those  of  Uranus, 
however,  are  already  defective,  probably  because  the 
discovery  of  that  planet  in  1781,  is  too  recent  to  admit 
of  much  precision  in  the  determination  of  its  motions, 
or  that  possibly  it  may  be  subject  to  disturbances  from 
some  unseen  planet  revolving  about  the  sun  beyond  the 
present  boundaries  of  our  system.  If,  after  a  lapse  of 
years,  the  tables  formed  from  a  combination  of  numer- 
ous observations  should  be  still  inadequate  to  represent 
the  motions  of  Uranus,  the  discrepancies  may  reveal 
the  existence,  nay  even  the  mass  and  orbit  of  a  body 
placed  forever  beyond  the  sphere  of  vision. 

The  tables  of  Mars,  Venus,  Mercury,  and  even  those 
of  the  sun,  have  been  greatly  improved,  and  still  occupy 
the  attention  of  Professor  Airy  and  other  distinguished 
astronomers.  We  are  chiefly  indebted  to  the  German 
astronomers  for  tables  of  the  four  new  planets,  which 
are  astonishingly  perfect,  considering  that  these  bodies 
have  not  been  discovered  more  than  forty  years,  and  a 
much  longer  time  is  requisite  to  develop  their  inequal- 
ities. 


SECTION  IX. 

Rotation  of  the  Sun  and  Planets — Saturn's  Rings — Periods  of  the  Rotation 
of  the  Moon  and  other  Satellites  equal  to  the  Periods  of  their  Revolu- 
tions— Form  of  Lunar  Spheroid — Libratjon,  Aspect,  and  Constitution  of 
the  Moon — Rotation  of  Jupiter's  Satellites. 

THE  oblate  form  of  several  ot  the  planets  indicates 
rotatory  motion.  This  has  been  confirmed  in  most 
cases  by  tracing  spots  on  their  surface,  by  which  their 
poles  and  times  of  rotation  have  been  determined.  The 
rotation  of  Mercury  is  unknown,  on  account  of  his  prox- 
imity to  the  sun ;  that  of  the  new  planets  has  not  yet 


SECT.  IX.          ROTATION  OF  SUN  AND  PLANETS.  61 

been  ascertained.  The  sun  revolves  in  twenty-five  days 
and  ten  hours  about  an  axis  which  is  directed  toward  a 
point  half-way  between  the  pole-star  and  Lyra,  the  plane 
of  rotation  being  inclined  by  7°  30',  or  a  little  more  than 
seven  degrees,  to  the  plane  of  the  ecliptic ;  it  may  there- 
fore be  concluded  that  the  sun's  mass  is  a  spheroid, 
flattened  at  the  poles.  From  the  rotation  of  the  sun, 
there  is  every  reason  to  believe  that  he  has  a  progres- 
sive motion  in  space,  although  the  direction  to  which  he 
tends  is  unknown ;  but,  in  consequence  of  the  reaction 
of  the  planets,  he  describes  a  small  irregular  orbit  about 
the  center  of  gravity  of  the  system,  never  deviating  from 
his  position  by  more  than  twice  his  own  diameter,  or  a 
little  more  than  seven  times  the  distance  of  the  moon 
from  the  earth.  The  sun  and  all  his  attendants  rotate 
from  west  to  east,  on  axes  that  remain  nearly  parallel 
to  themselves  (N.  137)  in  every  point  of  their  orbit,  and 
with  angular  velocities  that  are  sensibly  uniform  (N. 
138).  Although  the  uniformity  in  the  direction  of  their 
rotation  is  a  circumstance  hitherto  unaccounted  for  in 
the  economy  of  nature,  yet,  from  the  design  and  adapta- 
tion of  eveiy  other  part  to  the  perfection  of  the  whole, 
a  coincidence  so  remarkable  cannot  be  accidental ;  and 
as  the  revolutions  of  the  planets  and  satellites  are  also 
from  west  to  east,  it  is  evident  that  both  must  have 
arisen  from  the  primitive  cause  which  determined  the 
planetary  motions.  Indeed,  La  Place  has  computed 
the  probability  to  be  as  four  millions  to  one  that  all  the 
motions  of  the  planets,  both  of  rotation  and  revolution, 
were  at  once  imparted  by  an  original  common  cause, 
but  of  which  we  know  neither  the  nature  nor  the 
epoch. 

The  larger  planets  rotate  in  shorter  periods  than  the 
smaller  planets  and  the  earth.  Their  compression  is, 
consequently,  greater,  and  the  action  of  the  sun  and  of 
their  satellites  occasions  a  nutation  in  their  axes  and  a 
precession  of  their  equinoxes  (N.  144)  similar  to  that 
which  obtains  in  the  terrestrial  spheroid,  from  the  at- 
traction of  the  sun  and  moon  on  the  prominent  matter 
at  the  equator.  Jupiter  revolves  in  less  than  ten  hours 
about  an  axis  at  right  angles  to  certain  dark  belts,  or 
bands,  which  always  cross  his  equator.  This  rapid  rota- 
F 


62  SATURN  AND  HIS  RINGS.  SECT.  IX. 

tion  occasions  a  very  great  compression  in  his  form. 
His  equatorial  axis  exceeds  his  polar  axis  by  6000  miles, 
whereas  the  difference  in  the  axes  of  the  earth  is  only 
about  twenty-six  and  a  half.  It  is  an  evident  conse- 
quence of  Kepler's  law  of  the  squares  of  the  periodic 
times  of  the  planets  being  as  the  cubes  of  the  major 
axes  of  their  orbits,  that  the  heavenly  bodies  move 
slower  the  farther  they  are  from  the  sun.  In  compa- 
ring the  periods  of  the  revolutions  of  Jupiter  and  Saturn 
with  the  times  of  their  rotation,  it  appears  that  a  year 
of  Jupiter  contains  nearly  ten  thousand  of  his  days,  and 
that  of  Saturn  about  thirty  thousand  Saturnian  days. 

The  appearance  of  Saturn  is  unparalleled  in  the  sys- 
tem of  the  world.  He  is  a  spheroid  nearly  1000  times 
larger  than  the  earth,  surrounded  by  a  ring  even  brighter 
than  himself,  which  always  remains  suspended  in  the 
plane  of  his  equator ;  and,  viewed  with  a  very  good 
telescope,  it  is  found  to  consist  of  two  concentric  rings, 
divided  by  a  dark  band.  The  mean  distance  of  the 
interior  part  of  this  double  ring  from  the  surface  of  the 
planet  is  about  22,240  miles ;  it  is  no  less  than  33,360 
miles  broad,  but,  by  the  estimation  of  Sir  John  Herschel, 
its  thickness  does  not  much  exceed  300  miles,  so  that  it 
appears  like  a  plane.  By  the  laws  of  mechanics,  it  is 
impossible  that^this  body  can  retain  its  position  by  the 
adhesion  of  itsv  particles  alone.  It  must  necessarily 
revolve  with  a  velocity  that  will  generate  a  centrifugal 
force  sufficient  to  balance  the  attraction  of  Saturn!  Ob- 
servation confirms  the  truth  of  these  principles,  showing 
that  the  rings  rotate  from  west  to  east  about  the  planet 
in  ten  hours  and  a  half,  which  is  nearly  the  time  a  satel- 
lite would  take  to  revolve  about  Saturn  at  the  same  dis- 
tance. Their  plane  is  inclined  to  the  ecliptic,  at  an 
angle  of  28°  10'  44"-5  ;  in  consequence  of  this  obliquity 
of  position,  they  always  appear  elliptical  to  us,  but  with 
an  eccentricity  so  variable  as  even  to  be  occasionally  like 
a  straight  line  drawn  across  the  planet.  In  the  begin- 
ning of  October,  1832,  the  plane  of  the  rings  passed 
through  the  center  of  the  earth ;  in  that  position  they 
are  only  visible  with  very  superior  instruments,  and 
appear  like  a  fine  line  across  the  disc  of  Saturn.  About 
the  middle  of  December,  in  the  same  year,  the  rings 


S.CT.  IX.  ROTATION  OF  THE  MOON.  63 

became  visible  with  ordinary  instruments,  on  account  of 
their  plane  passing  through  the  sun.  In  the  end  of 
April,  1833,  the  rings  vanished  a  second  time,  and  re- 
appeared in  June  of  that  year.  Similar  phenomena 
will  occur  in  1847,  and  generally  as  often  as  Saturn  has 
the  same  longitude  with  either  node  of  his  rings.  Each 
side  of  these  rings  has  alternately  fifteen  years  of  sun- 
shine and  fifteen  years  of  darkness.  A  dark  line  has 
been  seen  in  the  outer  ring,  supposed  to  indicate  a  sub- 
division. 

It  is  a  singular  result  of  theory  that  the  rings  could 
not  maintain  their  stability  of  rotation  if  they  were 
everywhere  of  uniform  thickness  ;  for  the  smallest  dis- 
turbance would  destroy  the  equilibrium,  which  would 
become  more  and  more  deranged,  till  at  last  they  would 
be  precipitated  on  the  surface  of  the  planet.  The  rings 
of  Saturn  must,  therefore,  be  irregular  solids  of  unequal 
breadth  in  different  parts  of  the  circumference,  so  that 
their  centers  of  gravity  do  not  coincide  with  the  centers 
of  their  figures.  Professor  Strave  has  also  discovered 
that  the  center  of  the  ring  is  not  concentric  with  the 
center  of  Saturn.  The  interval  between  the  outer  edge 
of  the  globe  of  the  planet  and  the  outer  edge  of  the  ring 
on  one  side  is  11"'272,  and  on  the  other  side  the  inter- 
val is  11"-390,  consequently  there  is  an  eccentricity  of 
the  globe  in  the  ring  of  0"-215.  If  the  rings  obeyed 
different  forces  they  would  not  remain  in  the  same 
plane  ; '  but  the  powerful  attraction  of  Saturn  always 
maintains  them  and  his  satellites  in  the  plane  of  his 
equator.  The  rings,  by  their  mutual  action,  and  that 
of  the  sun  and  satellites,  must  oscillate  about  the  center 
of  Saturn,  and  produce  phenomena  of  light  and  shadow 
whose  periods  extend  to  many  years.  According  to  M. 
Bessel  the  mass  of  Saturn's  ring  is  equal  to  the  yfy  part 
of  that  of  the  planet. 

The  periods  of  rotation  of  the  moon  and  the  other 
satellites  are  equal  to  the  times  of  their  revolutions ; 
consequently  these  bodies  always  turn  the  same  face  to 
their  primaries.  However,  as  the  mean  motion  of  the 
moon  is  subject  to  a  secular  inequality  which  will  ulti- 
mately amount  to  many  circumferences  (N.  107),  if  the 
rotation  of  the  moon  were  perfectly  uniform  and  not 


64  ITERATIONS  OF  THE  MOON  SECT.  IX. 

affected  by  the  same  inequalities,  it  would  cease  exactly 
to  counterbalance  the  motion  of  revolution  ;  and  the 
moon,  in  the  course  of  ages,  would  successively  and 
gradually  discover  every  point  of  her  surface  to  the 
earth.  But  theory  proves  that  this  never  can  happen ; 
for  the  rotation  of  the  moon,  though  it  does  not  partake 
of  the  periodic  inequalities  of  her  revolution,  is  affected 
by  the  same  secular  variations,  so  that  her  motions  of 
rotation  and  revolution  round  the  earth  will  always 
balance  each  other  and  remain  equal.  This  circum- 
stance arises  from  the  form  of  the  lunar  spheroid,  which 
has  three  principal  axes  of  different  lengths  at  right 
angles  to  each  other. 

The  moon  is  flattened  at  her  poles  from  her  centri- 
fugal force  ;  therefore  her  polar  axis  is  the  least.  The 
other  two  are  in  the  plane  of  her  equator ;  but  that 
directed  toward  the  earth  is  the  greatest  (N.  139).  The 
attraction  of  the  earth,  as  if  it  had  drawn  out  that  part 
of  the  moon's  equator,  constantly  brings  the  greatest 
axis,  and,  consequently,  the  same  hemisphere,  toward 
us,  which  makes  her  rotation  participate  in  the  secular 
variations  of  her  mean  motion  of  revolution.  Even  if 
the  angular  velocities  of  rotation  and  revolution  had  not 
been  nicely  balanced  in  the  beginning  of  the  moon's 
motion,  the  attraction  of  the  earth  would  have  recalled 
the  greatest  axis  to  the  direction  of  the  line  joining  the 
centers  of  the  moon  and  earth,  so  that  it  would  have 
vibrated  on  each  side  of  that  line  in  the  same  manner  as 
a  pendulum  oscillates  on  each  side  of  the  vertical  from 
the  influence  of  gravitation.  No  such  libration  is  per- 
ceptible ;  and,  as  the  smallest  disturbance  would  make 
it  evident,  it  is  clear  that,  if  the  moon  has  ever  been 
touched  by  a  comet,  the  mass  of  the  latter  must  have 
been  extremely  small.  If  it  had  been  only  the  hundred 
thousandth  part  of  that  of  the  earth,  it  would  have  ren- 
dered the  libration  sensible.  According  to  analysis,  a 
similar  libration  exists  in  the  motions  of  Jupiter's  satel- 
lites, which  still  remains  insensible  to  observation,  and 
yet  the  comet  of  1770  passed  twice  through  the  midst 
of  them. 

The  moon,  it  is  true,  is  liable  to  librations  depending 
upon  the  position  of  the.  spectator.  At  her  rising,  part 


SBCT.  IX.    ROTATION  OF  JUPITER'S  SATELLITES.  65 

9 

of  the  western  edge  of  her  disc  is  visible,  which  is  in- 
visible at  her  setting,  and  the  contrary  takes  place  with 
regard  to  her  eastern  edge.  There  are  also  librations 
arising  from  the  relative  positions  of  the  earth  and 
moon  in  their  respective  orbits ;  but  as  they  are  only 
optical  appearances,  one  hemisphere  will  be  eternally 
concealed  from  the  earth.  For  the  same  reason,  the 
earth,  which  must  be  so  splendid  an  object  to  one  lunar 
hemisphere,  will  be  forever  veiled  from  the  other.  On 
account  of  these  circumstances,  the  remoter  hemi- 
sphere of  the  moon  has  its  day  a  fortnight  long,  and  a 
night  of  the  same  duration,  not  even  enlightened  by  a 
moon,  while  the  favored  side  is  illuminated  by  the  re- 
flection of  the  earth  during  its  long  night.  A  planet 
exhibiting  a  surface  thirteen  times  larger  than  that  of 
the  moon,  with  all  the  varieties  of  clouds,  land,  and 
water  coming  successively  into  view,  must  be  a  splen- 
did object  to  a  lunar  traveler  in  a  journey  to  his  an- 
tipodes. The  great  height  of  the  lunar  mountains  prob- 
ably has  a  considerable  influence  on  the  phenomena  of 
her  motion,  the  more  so  as  her  compression  is  small, 
and  her  mass  considerable.  In  the  curve  passing 
through  the  poles,  and  that  diameter  of  the  moon  which 
always  points  to  the  earth,  nature  has  furnished  a  per- 
manent meridian,  to  which  the  different  spots  on  her 
surface  hare  been  referred,  and  their  positions  are  de- 
termined with  as  much  accuracy  as  those  of  many  of 
the  most  remarkable  places  on  the  surface  of  our  globe. 
The  distance  and  minuteness  of  Jupiter's  satellites 
render  it  extremely  difficult  to  ascertain  their  rotation. 
It  was,  however,  accomplished  by  Sir  William  Herschel 
from  their  relative  brightness.  He  observed  that  they 
alternately  exceeded  each  other  in  brilliancy,  and,  by 
comparing  the  maxima  and  minima  of  then'  illumination 
with  their  positions  relatively  to  the  sun  and  to  their 
primary,  he  found  that  like  the  moon  the  time  of  their 
rotation  is  equal  to  the  period  of  their  revolution  about 
Jupiter.  Miraldi  was  led  to  the  same  conclusion  with 
regard  to  the  fourth  satellite,  from  the  motion  of  a  spot 
on  its  surface. 

5  F3 


66  ROTATION  OF  THE  EARTH.  SECT.  X. 


SECTION  X. 

Rotation  of  the  Earth  invariable — Decrease  in  the  Earth's  Mean  Tempera- 
ture—Earth originally  in  a  State  of  Fusion— Length  of  Day  constant- 
Decrease  of  Temperature  ascribed  by  Sir  John  Herschel  to  the  Variation 
in  the  Eccentricity  of  the  Terrestrial  Orbit — Difference  in  the  Tempera- 
ture of  the  Two  Hemispheres,  erroneously  ascribed  to  the  Excess  in  the 
Length  of  Spring  and  Summer  in  the  Southern  Hemisphere  ;  attributed 
by  Mr.  Lyell  to  the  Operation  of  existing  Causes— Three  Principal  Axes 
of  Rotation — Position  of  the  Axis  of  Rotation  on  the  Surface  of  the  Earth 
invariable — Ocean  not  sufficient  to  restore  the  Equilibrium  of  the  Earth 
if  deranged — Its  Density  and  Mean  Depth — Internal  Structure  of  the 
Earth. 

THE  rotation  of  the  earth,  which  determines  the  length 
of  the  day,  may  be  regarded  as  one  of  the  most  import- 
ant elements  in  the  system  of  the  world.  It  serves  as 
a  measure  of  time,  and  forms  the  standard  of  com- 
parison for  the  revolutions  of  the  celestial  bodies,  which 
by  their  proportional  increase  or  decrease  would  soon 
disclose  any  changes  it  might  sustain.  Theory  and 
observation  concur  in  proving  that -among  the  innumer- 
able vicissitudes  which  prevail  throughout  creation,  the 
period  of  the  earth's  diurnal  rotation  is  immutable. 
The  water  of  rivers,  falling  from  a  higher  to  a  lower 
level,  carries  with  it  the  velocity  due  to  its  revolution 
with  the  earth  at  a  greater  distance  from  the  center ;  it 
will  therefore  accelerate,  although  to  an  almost  infinites- 
imal extent,  the  earth's  daily  rotation.  The  sum  of  all 
these  increments  of  velocity  arising  from  the  descent  of 
all  the  rivers  on  the  earth's  surface  would  in  time  be- 
come perceptible,  did  not  nature  by  the  process  of  evap- 
oration raise  the  waters  back  to  their  sources  ;  and  thus, 
by  again  removing  matter  to  a  greater  distance  from 
the  center,  destroy  the  velocity  generated  by  its  pre- 
vious approach ;  so  that  the  descent  of  rivers  does  not 
affect  the  earth's  rotation.  Enormous  masses  projected 
by  volcanos  from  the  equator  to  the  poles,  and  the  con- 
trary, would  indeed  affect  it,  but  there  is  no  evidence  of 
such  convulsions.  The  disturbing  action  of  the  moon 
and  planets,  which  has  so  powerful  an  effect  on  the 
revolution  of  the  earth,  in  no  way  influences  its  rota- 
tion. The  constant  friction  of  the  trade-winds  on  the 


SECT.  X.  INVARIABILITY  OF  ROTATION.  (ft 

mountains  and  continents  between  the  tropics  does  not 
impede  its  velocity,  which  theory  even  proves  to  be  the 
same  as  if  the  sea  together  with  the  earth  formed  one 
solid  mass.  But  although  these  circumstances  be  in- 
sufficient, a  variation  in  the  mean  temperature  would 
certainly  occasion  a  corresponding  change  in  the  velocity 
of  rotation.  In  the  science  of  dynamics  it  is  a  principle 
in  a  system  of  bodies  or  of  particles  revolving  about  a 
fixed  center,  that  the  momentum  or  sum  of  the  pro- 
ducts of  the  mass  of  each  into  its  angular  velocity  and 
distance  from  the  center  is  a  constant  quantity,  if  the 
system  be  not  deranged  by  a  foreign  cause.  Now  since 
the  number  of  particles  in  the  system  is  the  same  what- 
ever its  temperature  may  be,  when  their  distances  from 
the  center  are  diminished  then-  angular  velocity  must 
be  increased,  in  order  that  the  preceding  quantity  may 
still  remain  constant.  It  follows  then  that  as  the  primi- 
tive momentum  of  rotation  with  which  the  earth  was 
projected  into  space  must  necessarily  remain  die  same, 
the  smallest  decrease  in  heat  by  contracting  the  terres- 
trial spheroid  would  accelerate  its  rotation,  and  conse- 
quently diminish  the  length  of  the  day.  Notwithstand- 
ing the  constant  accession  of  heat  from  the  sun's  rays, 
geologists  have  been  induced  to  believe  from  the  fossil 
remains,  that  the  mean  temperature  of  the  globe  is  de- 
creasing. 

The  high  temperature  of  mines,  hot  springs,  and 
above  all  the  internal  fires  which  have  produced  and  do 
still  occasion  such  devastation  on  our  planet,  indicate  an 
augmentation  of  heat  toward  its  center.  The  increase 
of  density  corresponding  to  the  depth  and  the  form  of 
the  spheroid  being  what  theory  assigns  to  a  fluid  mass 
in  rotation,  concurs  to  induce  the  idea  that  the  tempera- 
ture of  the  earth  was  originally  so  high  as  to  reduce  all 
the  substances  of  which  it  is  composed  to  a  state  of 
fusion  or  of  vapor,  and  that  in  the  course  of  ages  it  has 
cooled  down  to  its  present  state ;  that  it  is  still  becoming 
colder,  and  that  it  will  continue  to  do  so  till  the  whole 
mass  arrives  at  the  temperature  of  the  medium  in 
which  it  is  placed,  or  rather  at  a  state  of  equilibrium 
between  this  temperature,  the  cooling  power  of  its  own 
radiation,  and  the  heating  effect  of  the  sun's  rays.  . 


68  DECREASE  OF  TEMPERATURE.  SJCCT.  X. 

Previous  to  the  formation  of  ice  at  the  poles,  the 
ancient  lands  of  northern  latitudes  might  no  doubt  have 
been  capable  of  producing  those  tropical  plants  pre- 
served in  the  coal-measures,  if  indeed  such  plants  could 
flourish  without  the  intense  light  of  a  tropical  sun.  But 
even  if  the  decreasing  temperature  of  the  earth  be 
sufficient  to  produce  the  observed  effects,  it  must  be 
extremely  slow  in  its  operation ;  for  in  consequence  of 
the  rotation  of  the  earth  being  a  measure  of  the  periods 
of  the  celestial  motions,  it  has  been  proved  that  if  the 
length  of  the  day  had  decreased  by  the  three-thou- 
sandth part  of  a  second  since  the  observations  of  Hippar- 
chus  two  thousand  years  ago,  it  would  have  diminished 
the  secular  equation  of  the  moon  by  4"'4.  It  is  there- 
fore beyond  a  doubt  that  the  mean  temperature  of  the 
earth  cannot  have  sensibly  varied  during  that  time.  If 
then  the  appearances  exhibited  by  the  strata  are  really 
owing  to  a  decrease  of  internal  temperature,  it  either 
shows  the  immense  periods  requisite  to  produce  geo- 
logical changes,  to  which  two  thousand  years  are  as 
nothing,  or  that  the  mean  temperature  of  the  earth  had 
arrived  at  a  state  of  equilibrium  before  these  observa- 
tions. 

However  strong  the  indications  of  the  primitive 
fluidity  of  the  earth,  as  there  is  no  direct  proof  of  it, 
the  hypothesis  can  only  be  regarded  as  very  probable. 
But  one  of  the  most  profound  philosophers  and  elegant 
writers  of  modern  times  has  found  in  the  secular  varia- 
tion of  the  eccentricity  of  the  terrestrial  orbit  an  evident 
cause  of  decreasing  temperature.  That  accomplished 
author,  in  pointing  out  the  mutual  dependencies  of  phe- 
nomena, says,  "  It  is  evident  that  the  mean  temperature 
of  the  whole  surface  of  the  globe,  in  so  far  as  it  is  main- 
tained by  the  action  of  the  sun  at  a  higher  degree  than 
it  would  have  were  the  sun  extinguished,  must  depend 
on  the  mean  quantity  of  the  sun's  rays  which  it  re- 
ceives, or — which  comes  to  the  same  thing — on  the 
total  quantity  received  in  a  given  invariable  time ;  and 
the  length  of  the  year  being  unchangeable  in  all  the 
fluctuations  of  the  planetary  system,  it  follows  that  the 
total  amount  of  solar  radiation  will  determine,  cceteris 
paribus,  the  general  climate  of  the  earth.  Now,  it  is 


SECT.  X.  DECREASE  OF  TEMPERATURE.  69 

not  difficult  to  show  that  this  amount  is  inversely  pro- 
portional to  the  minor  axis  of  the  ellipse  described  by 
the  earth  about  the  sun  (N.  140),  regarded  as  slowly 
variable  ;  and  that,  therefore,  the  major  axis  remaining, 
as  we  know  it  to  be  constant,  and  the  orbit  being  actu- 
ally in  a  state  of  approach  to  a  circle,  and  consequently 
the  minor  axis  being  on  the  increase,  the  mean  annual 
amount  of  solar  radiation  received  by  the  whole  earth 
must  be  actually  on  the  decrease.  We  have  therefore 
an  evident  real  cause  to  account  for  the  phenomenon." 
The  limits  of  the  variation  in  the  eccentricity  of  the 
earth's  orbit  are  unknown.  But  if  its  ellipticity  has 
ever  been  as  great  as  that  of  the  orbit  of  Mercury  or 
Pallas,  the  mean  temperature  of  the  earth  must  Jaave 
been  sensibly  higher  than  it  is  at  present.  Whether  it 
was  great  enough  to  render  our  northern  climates  fit 
for  the  production  of  tropical  plants,  and  for  the  resi- 
dence of  the  elephant  and  other  animals  now  inhabitants 
of  the  torrid  zone,  it  is  impossible  to  say. 

Of  the  decrease  in  temperature  of  the  northern 
hemisphere  there  is  abundant  evidence  in  the  fossil 
plants  discovered  in  very  high  latitudes,  which  could 
only  have  existed  in  a  tropical  climate,  and  which  must 
have  grown  near  the  spot  where  they  are  found,  from 
the  delicacy  of  their  structure  and  the  perfect  state  of 
their  preservation.  This  change  of  temperature  has 
been  erroneously  ascribed  to  an  excess  in  the  duration 
of  spring  and  summer  in  the  northern  hemisphere,  in 
consequence  of  the  eccentricity  of  the  solar  ellipse. 
The  length  of  the  seasons  varies  with  the  position  of 
the  perihelion  (N.  64)  of  the  earth's  orbit  for  two 
reasons.  On  account  of  the  eccentricity,  small  as  it  is, 
any  line  passing  through  the  center  of  the  sun  divides 
the  terrestrial  ellipse  into  two  unequal  parts,  and  by  the 
laws  of  elliptical  motion  the  earth  moves  through  these 
two  portions  with  unequal  velocities.  The  perihelion 
always  lies  in  the  smaller  portion,  and  there  the  earth's 
motion  is  the  most  rapid.  In  the  present  position  of 
the  perihelion,  spring  and  summer  north  of  the  equator 
exceed  by  about  eight  days  the  duration  of  the  same 
seasons  south  of  it.  And  10,492  years  ago  the  southern 
hemisphere  enjoyed  the  advantage  we  now  possess 


70  CAUSES  AFFECTING  THE  TEMPERATURE.    SECT.  X. 

from  the  secular  variation  of  the  perihelion.  Yet  Sir 
John  Herschel  has  shown  that  by  this  alteration  neither 
hemisphere  acquires  any  excess  of  light  or  heat  above 
the  other ;  for  although  the  earth  is  nearer  to  the  sun 
while  moving  through  that  part  of  its  orbit  in  which  the 
perihelion  lies  than  in  the  other  part,  and  consequently 
receives  a  greater  quantity  of  light  and  heat,  yet  as  it 
moves  faster  it  is  exposed  to  the  heat  for  a  shorter 
time.  In  the  other  part  of  the  orbit,  on  the  contrary, 
the  earth  being  farther  from  the  sun  receives  fewer  of 
his  rays,  but  because  its  motion  is  slower  it  is  exposed 
to  them  for  a  longer  time.  And  as  in  both  cases  the 
quantity  of  heat  and  the  angular  velocity  vary  exactly  in 
the  same  proportion,  a  perfect  compensation  takes  place 
(N.  141).  So  that  the  eccentricity  of  the  earth's  orbit 
has  little  or  no  effect  on  the  temperature  corresponding 
to  the  difference  of  the  seasons. 

Mr.  Lyell,  in  his  excellent  work  on  Geology,  refers 
the  increased  cold  of  the  northern  hemisphere  to  the 
operation  of  existing  causes,  with  more  probability  than 
most  theories  that  have  been  advanced  in  solution  of 
this  difficult  subject.  The  loftiest  mountains  would  be 
represented  by  a  grain  of  sand  on  a  globe  six  feet  in 
diameter,  and  the  depth  of  the  ocean  by  a  scratcl^  on 
its  surface.  Consequently  the  gradual  elevation  of  a 
continent  or  chain  of  mountains  above  the  surface  of  the 
ocean,  or  their  depression  below  it,  is  no  very  great 
event  compared  with  the  magnitude  of  the  earth,  and 
the  energy  of  its  subterranean  fires,  if  the  same  periods 
of  time  be  admitted  in  the  progress  of  geological  as  in 
astronomical  phenomena,  which  the  successive  and  va- 
rious races  of  extinct  beings  show  to  have  been  immense. 
Climate  is  always  more  intense  in  the  interior  of  con- 
tinents than  in  islands  or  sea-coasts.  An  increase  of 
land  within  the  tropics  would  therefore  augment  the 
general  heat,  and  an  increase  in  the  temperate  and 
frigid  zones  would  render  the  cold  more  severe.  Now 
it  appears  that  most  of  the  European,  North  Asiatic, 
and  North  American  continents  and  islands  were  raised 
from  the  deep  after  the  coal-measures  were  formed  in 
which  the  fossil  tropical  plants  are  found ;  and  a  variety 
of  geological  facts  indicate  the  existence  of  an  ancient 


Sxrr.  X.  AXIS  OP  ROTATION  INVARIABLE.  71 

and  extensive  archipelago  throughout  the  greater  part 
of  the  northern  hemisphere.  Mr.  Lyell  is  therefore  of 
opinion  that  the  climate  of  these  islands  must  have 
been  sufficiently  mild  in  consequence  of  the  surrounding 
ocean  to  clothe  them  with  tropical  plants,  and  render 
them  a  fit  abode  for  the  huge  animals  whose  fossil 
remains  are  so  often  found.  That  the  arborescent  ferns 
and  the  palms  of  these  regions,  carried  by  streams  to 
the  bottom  of  the  ocean,  were  imbedded  in  the  strata 
which  were  by  degrees  heaved  up  by  the  subterranean 
fires  during  a  long  succession  of  ages,  till  the  greater 
part  of  the  northern  hemisphere  became  dry  land  as  it 
now  is,  and  that  the  consequence  has  been  a  continual 
decrease  of  temperature. 

It  is  evident  from  the  marine  shells  found  on  the  tops 
of  the  highest  mountains  and  in  almost  every  part  of 
the  globe,  that  immense  continents  have  been  elevated 
above  the  ocean,  which  must  have  ingulfed  others. 
Such  a  catastrophe  would  be  occasioned  by  a  variation 
in  the  position  of  the  axis  of  rotation  on  the  surface  of 
the  earth ;  for  the  seas  tending  to  a  new  equator  would 
leave  some  portions  of  the  globe  and  overwhelm  others. 
Now,  it  is  found  by  the  laws  of  mechanics  that  in  every 
body,  be  its  form  or  density  what  it  may,  there  are  at 
least  three  axes  at  right  angles  to  each  other,  round 
any  one  of  which,  if  the  solid  begins  to  rotate,  it  will 
continue  to  revolve  forever,  provided  it  be  not  disturbed 
by  a  foreign  cause,  but  that  the  rotation  about  any 
other  axis  will  only  be  for  an  instant,  and  consequently 
the  poles  or  extremities  of  the  instantaneous  axis  of 
rotation  would  perpetually  change  their  position  on  the 
surface  of  the  body.  In  an  ellipsoid  of  revolution  the 
polar  diameter  and  every  diameter  in  the  plane  of  the 
equator  are  the  only  permanent  axes  of  rotation  (N. 
142).  Hence  if  the  ellipsoid  were  to  begin  to  revolve 
about  any  diameter  between  the  pole  and  the  equator, 
the  motion  would  be  so  unstable  that  the  axis  of  rota- 
tion and  the  position  of  the  poles  would  change  every 
instant.  Therefore  as  the  earth  does  not  differ  much 
from  this  figure,  if  it  did  not  turn  round  one  of  its  prin- 
cipal axes,  the  position  of  the  poles  would  change  daily ; 
the  equator,  which  is  90°  distant,  would  undergo  cor- 


72  AXIS  OF  ROTATION  INVARIABLE.  Sfccr.  X. 

responding  variations ;  and  the  geographical  latitudes  of 
all  places  being  estimated  from  the  equator,  assumed  to 
be  fixed,  would  be  perpetually  changing.  A  displace- 
ment in  the  position  of  the  poles  of  only  two  hundred 
miles  would  be  sufficient  to  produce  these  effects,  and 
would  immediately  be  detected.  But  as  the  latitudes 
are  found  to  be  invariable,  it  may  be  concluded  that  the 
terrestrial  spheroid  must  have  revolved  about  the  same 
axis  for  ages.  The  earth  and  planets  differ  so  little 
from  ellipsoids  of  revolution,  that  in  all  probability  any 
libration  from  one  axis  to  another  produced  by  the 
primitive  impulse  which  put  them  in  motion,  must  have 
ceased  soon  after  their  creation  from  the  friction  of  the 
fluids  at  their  surface. 

Theory  also  proves  that  neither  nutation,  precession, 
nor  any  of  the  disturbing  forces  that  affect  the  system, 
have  the  smallest  influence  on  the  axis  of  rotation,  which 
maintains  a  permanent  position  on  the  surface,  if  the 
earth  be  not  disturbed  in  its  rotation  by  a  foreign  cause, 
as  the  collision  of  a  comet,  which  might  have  happened 
in  the  immensity  of  time.  But  had  that  been  the  case, 
its  effects  would  still  have  been  perceptible  in  .the  varia- 
tions of  the  geographical  latitudes.  If  we  suppose  that 
such  an  event  had  taken  place,  and  that  the  disturbance 
had  been  very  great,  equilibrium  could  then  only  have 
been  restored  with  regard  to  a  new  axis  of  rotation  by 
the  rushing  of  the  seas  to  the  new  equator,  which  they 
must  have  continued  to  do  till  the  surface  was  every- 
where perpendicular  to  the  direction  of  gravity.  But  it 
is  probable  that  such  an  accumulation  of  the  waters 
would  not  be  sufficient  to  restore  equilibrium  if  the  de- 
rangement had  been  great,  for  the  mean  density  of  the 
sea  is  only  about  a  fifth  part  of  the  mean  density  of  the 
earth,  and  the  mean  depth  of  the  Pacific  Ocean  is  sup- 
posed not  to  be  more  than  four  or  five  miles,  whereas 
the  equatorial  diameter  of  the  earth  exceeds  the  polar 
diameter  by  about  26i  miles.  Consequently  the  influ- 
ence of  the  sea  on  the  direction  of  gravity  is  veiy  small. 
And  as  it  thus  appears  that  a  great  change  in  the  posi- 
tion of  the  axis  is  incompatible  with  the  law  of  equilib- 
rium, the  geological  phenomena  in  question  must  be 
ascribed  to  an  internal  cause.  Indeed  it  is  now  demon- 


S«cr.  X.        INTERNAL  DENSITY  OF  THE  EARTH.  73 

strated  that  the  strata  containing  marine  diluvia  which 
are  in  lofty  situations,  must  have  been  formed  at  the 
bottom  of  the  ocean  and  afterward  upheaved  by  the 
action  of  subterraneous  fires.  Besides,  it  is  clear  from 
the  mensuration  of  the  arcs  of  the  meridian  and  the 
length  of  the  seconds'  pendulum,  as  well  as  from  the 
lunar  theory,  that  the  internal  strata  and  also  the  exter- 
nal outline  of  the  globe  are  elliptical,  their  centers  being 
coincident  and  their  axes  identical  with  that  of  the  sur- 
face— a  state  of  things  which,  according  to  the  distin- 
guished author  lately  quoted,  is  incompatible  with  a 
subsequent  accommodation  of  the  surface  to  a  new  and 
different  state  of  rotation  from  that  which  determined 
the  original  distribution  of  the  component  matter.  Thus 
amid  the  mighty  revolutions  which  have  swept  innumer- 
able races  of  organized  beings  from  the  earth,  which 
have  elevated  plains  and  buried  mountains  in  the  ocean, 
the  rotation  of  the  earth  and  the  position  of  the  axis  on 
its  surface  have  undergone  but  slight  variations. 

The  strata  of  the  terrestrial  spheroid  are  not  only 
concentric  and  elliptical,  but  the  lunar  inequalities  show 
that  they  increase  in  density  from  the  surface  of  the 
earth  to  its  center.  This  would  certainly  have  happened 
if  the  earth  had  originally  been  fluid,  for  the  denser  parts 
must  have  subsided  toward  the  center  as  it  approached 
a  state  of  equilibrium.  But  the  enormous  pressure  of 
the  superincumbent  mass  is  a  sufficient  cause  for  the 
phenomenon.  Professor  Leslie  observes  that  air  com- 
pressed into  the  fiftieth  part  of  its  volume  has  its  elas- 
ticity fifty  times  augmented.  If  it  continues  to  contract 
at  that  rate,  it  would,  from  its  own  incumbent  weight, 
acquire  the  density  of  water  at  the  depth  of  thirty-four 
miles.  But  water  itself  would  have  its  density  doubled 
at  the  depth  of  ninety-three  miles,  and  would  even  at- 
tain the  density  of  quicksilver  at  a  depth  of  362  miles. 
Descending  therefore  toward  the  center  through  nearly 
4000  miles,  the  condensation  of  ordinary  substances 
would  surpass  the  utmost  powers  of  conception.  Dr. 
Young  says  that  steel  would  be  compressed  into  one- 
fourth  and  stone  into  one-eighth  of  its  bjilk  at  the  earth's 
center.  However,  we  are  yet  ignorant  of  the  laws  of 
compression  of  solid  bodies  beyond  a  Certain  limit ;  from 
G 


74  PRECESSION.  SECT.  XI. 

the  experiments  of  Mr.  Perkins  they  appear  to  be  ca- 
pable of  a  greater  degree  of  compression  than  has  gen- 
erally been  imagined. 

But  a  density  so  extreme  is  not  borne  out  by  astro- 
nomical observation.  It  might  seem  to  follow,  there- 
fore, that  our  planet  must  have  a  widely  cavernous 
structure,  and  that  we  tread  on  a  crust  or  shell  whose 
thickness  bears  a  very  small  proportion  to  the  diameter 
of  its  sphere.  Possibly,  too,  this  great  condensation  at 
the  central  regions  may  be  counterbalanced  by  the  in- 
creased elasticity  due  to  a  very  elevated  temperature. 


SECTION  XI. 

Precession  and  Nutation — Their  Effects  on  the  Apparent  Places  of  the 
Fixed  Stars. 

IT  has  been  shown  that  the  axis  of  rotation  is  invari- 
able on  the  surface  of  the  earth ;  and  observation  as  well 
as  theory  prove  that  were  it  not  for  the  action  of  the 
sun  and  moon  on  the  matter  at  the  equator,  it  would 
remain  exactly  parallel  to  itself  in  every  point  of  its  orbit. 

The  attraction  of  an  external  body  not  only  draws  a 
spheroid  toward  it,  but  as  the  force  varies  inversely  as 
the  square  of  the  distance,  it  gives  it  a  motion  about  its 
center  of  gravity,  unless  when  the  attracting  body  is  sit- 
uated in  the  prolongation  of  one  of  the  axes  of  the  sphe- 
roid. The  plane  of  the  equator  is  inclined  to  the  plane 
of  the  ecliptic  at  an  angle  of  23°  27'  34"-69  ;  and  the 
inclination  of  the  lunar  orbit  to  the  same  is  5°  8'  4 1"' 9. 
Consequently,  from  the  oblate  figure  of  the  earth,  the 
sun  and  moon  acting  obliquely  and  unequally  on  the  dif- 
ferent parts  of  the  terrestrial  spheroid,  urge  the  plane 
of  the  equator  from  its  direction  and  force  it  to  move 
from  east  to  west,  so  that  the  equinoctial  points  have  a 
slow  retrograde  motion  on  the  plane  of  the  ecliptic,  of 
50"-41  annually.  The  direct  tendency  of  this  action  is 
to  make  the  planes  of  the  equator  and  ecliptic  coincide, 
but  it  is  balanced  by  the  tendency  of  the  earth  to  return 
to  stable  rotation  about  the  polar  diameter,  which  is  one 
of  its  principal  axes  of  rotation.  Therefore  the  inclina- 


S«CT.  XI.  PRECESSION.  75 

tion  of  the  two  planes  remains  constant,  as  a  top  spin- 
ning preserves  the  same  inclination  to  the  plane  of  the 
horizon.  Were  the  earth  spherical,  this  effect  would 
not  be  produced,  and  the  equinoxes  would  always  cor- 
respond with  the  same  points  of  the  ecliptic,  at  least  as 
far  as  this  kind  of  motion  is  concerned.  But  another 
and  totally  different  cause  which  operates  on  this  motion 
has  already  been  mentioned.  The  action  of  the  planets 
on  one  another  and  on  the  sun  occasions  a  very  slow  va- 
riation in  the  position  of  the  plane  of  the  ecliptic,  which 
uffects  its  inclination  to  the  plane  of  the  equator,  and 
gives  the  equinoctial  points  a  slow  but  direct  motion  on 
the  ecliptic  of  0"-31  annually,  which  is  entirely  inde- 
pendent of  the  figure  of  the  earth,  and  would  be  the 
same  if  it  were  a  sphere.  Thus  the  sun  and  moon,  by 
moving  the  plane  of  the  equator,  cause  the  equinoctial 
points  to  retrograde  on  the  ecliptic ;  and  the  planets  by 
moving  the  plane  of  the  ecliptic  give  them  a  direct  mo- 
tion, though  much  less  than  the  former.  Consequently 
the  difference  of  the  two  is  the  mean  precession,  which 
is  proved  both  by  theory  and  observation  to  be  about 
50"-1  annually  (N.  143). 

As  the  longitudes  of  all  the  fixed  stars  are  increased 
by  this  quantity,  the  effects  of  precession  are  soon  de- 
tected. It  was  accordingly  discovered  by  Hipparchus 
in  the  year  128  before  Christ,  from  a  comparison  of  his 
own  observations  with  those  of  Timocharis  155  years 
before.  In  the  time  of  Hipparchus,  the  entrance  of  the 
sun  into  the  constellation  Aries  was  the  beginning  of 
spring,  but  since  that  time  the  equinoctial  points  have 
receded  30°,  so  that  the  constellations  called  the  signs 
of  the  zodiac  are  now  at  a  considerable  distance  from 
those  divisions  of  the  ecliptic  which  bear  their  names. 
Moving  at  the  rate  of  50"- 1  annually,  the  equinoctial 
points  will  accomplish  a  revolution  in  25,868  years. 
But  as  the  precession  varies  in  different  centuries  the 
extent  of  this  period  will  be  slightly  modified.  Since 
the  motion  of  the  sun  is  direct,  and  that  of  the  equinoc- 
tial points  retrograde,  he  takes  a  shorter  time  to  return 
to  the  equator  than  to  arrive  at  the  same  stars ;  so  that 
the  tropical  year  of  365d  5h  48m  498'7  must  be  increased 
by  the  time  he  takes  to  move  through  an  arc  of  50"- 1, 


76  LENGTH  OF  THE  YEAR.  SECT.  XI. 

in  order  to  have  the  length  of  the  sidereal  year.  The 
time  required  is  20m  19s- 6,  so  that  the  sidereal  year  con- 
tains 365d  6h  9m  98-6  mean  solar  days. 

The  mean  annual  precession  is  subject  to  a  secular 
variation ;  for  although  the  change  in  the  plane  of  the 
ecliptic  in  which  the  orbit  of  the  sun  lies  be  independent 
of  the  form  of  the  earth,  yet  by  bringing  the  sun,  moon, 
and  earth  into  different  relative  positions  from  age  to 
age,  it  alters  the  direct  action  of  the  .two  first  on  the 
prominent  matter  at  the  equator :  on  this  account  the 
motion  of  the  equinox  is  greater,  by  0"-455  now  than  it 
was  in  the  time  of  Hipparchus.  Consequently  the  ac- 
tual length  of  the  tropical  year  is  about  4S>21  shorter 
than  it  was  at  that  time.  The  utmost  change  that  it 
can  experience  from  this  cause  amounts  to  43  seconds. 

Such  is  the  secular  motion  of  the  equinoxes.  But  it 
is  sometimes  increased  and  sometimes  diminished  by 
periodic  variations,  whose  periods  depend  upon  the 
relative  positions  of  the  sun  and  moon  with  regard  to 
the  earth,  and  which  are  occasioned  by  the  direct  ac- 
tion of  these  bodies  on  the  equator.  Dr.  Bradley  discov- 
ered that  by  this  action  the  moon  causes  the  pole  of  the 
equator  to  describe  a  small  ellipse  in  the  heavens,  the 
axes  of  which  are  18"-5  and  13"-674,  the  longer  being 
directed  toward  the  pole  of  the  ecliptic.  The  period 
of  this  inequality  is  about  19  years,  the  time  employed 
by  the  nodes  of  the  lunar  orbit  to  accomplish  a  revolu- 
tion. The  sun  causes  a  small  variation  in  the  descrip- 
tion of  this  ellipse ;  it  runs  through  its  period  in  half  a 
year.  Since  the  whole  earth  obeys  these  motions  they 
affect  the  position  of  its  axis  of  rotation  with  regard  to 
the  starry  heavens,  though  not  with  regard  to  the  sur- 
face of  the  earth;  for  in  consequence  of  precession 
alone  the  pole  of  the  equator  moves  in  a  circle  round 
the  pole  of  the  ecliptic  in  25,868  years,  and  by  nutation 
alone  it  describes  a  small  ellipse  in  the  heavens  every 
19  years,  on  each  side  of  which  it  deviates  every  half 
year  from  the  action  of  the  sun.  The  real  curve  traced 
in  the  starry  heavens  by  the  imaginary  prolongation  of 
the  earth's  axis  is  compounded  of  these  three  motions 
(N.  144).  This  nutatiou  in  the  earth's  axis  affects  both 
tho  precession  and  obliquity  with  small  periodic  varia- 


SECT.  XH.  EFFECTS  OF  NUTATION.  77 

tions.  But  in  consequence  of  the  secular  variation  in 
the  position  of  the  terrestrial  orbit,  which  is  chiefly 
owing  to  the  disturbing  energy  of  Jupiter  on  the  earth, 
the  obliquity  of  the  ecliptic  is  annually  diminished,  ac- 
cording to  M.  Bessel,  by  0"-457.  This  variation  in  the 
course  of  ages  may  amount  to  10  or  11  degrees ;  but  the 
obliquity  of  the  ecliptic  to  4he  equator  can  never  vary 
more  than  2°  42'  or  3°,  since  the  equator  will  follow  in 
some  measure  the  motion  of  the  ecliptic. 

It  is  evident  that  the  places  of  all  the  celestial  bodies 
are  affected  by  precession  and  nutation.  Their  longi- 
tudes estimated  from  the  equinox  are  augmented  by 
precession  ;  but  as  it  effects  all  the  bodies  equally,  it 
makes  no  change  in  their  relative  positions.  Both  the 
celestial  latitudes  and  longitudes  are  altered  to  a  small 
degree  by  nutation ;  hence  all  observations  must  be 
corrected  for  these  inequalities.  In  consequence  of  this 
real  motion  in  the  earth's  axis  the  pole  star,  forming 
part  of  the  constellation  of  the  Little  Bear,  which  was 
formerly  12°  from  the  celestial  pole,  is  now  within  1°  24' 
of  it,  and  will  continue  to  approach  it  till  it  is  within  £°, 
after  which  it  will  retreat  from  the  pole  for  ages;  and 
12,934  years  hence  the  star  a  Lyrae  will  come  within 
5°  of  the  celestial  pole,  and  become  the  polar  star  of 
the  northern  hemisphere. 


SECTION  XII. 

•Mfean  and  Apparent  Sidereal  Time— Mean  and  Apparent  Solar  Time — 
Equation  of  Time — English  and  French  Subdivisions  of  Time — Leap 
Year — Christian  Era — Equinoctial  Time — Remarkable  Eras  depending 
upon  the  Position  of  the  Solar  Perigee — Inequality  of  the  Lengths  of 
the  Seasons  in  the  two  Hemispheres — Application  of  Astronomy  to  Chro- 
nology— English  and  French  Standards  of  Weights  and  Measures. 

ASTRONOMY  has  been  of  immediate  and  essential  use 
in  affording  invariable  standards  for  measuring  duration, 
distance,  magnitude,  and  velocity.  The  mean  sidereal 
day  measured  by  the  time  elapsed  between  two  consec- 
utive transits  of  any  star  at  the  same  meridian,  and  the 
mean  sidereal  year,  which  is  the  time  included  between 
two  consecutive  returns  of  the  sun  to  the  same  star, 
are  immutable  units  with  which  all  great  periods  of 
02 


78  SOLAR  TIME.  SECT.  XII. 

time  are  compared ;  the  oscillations  of  the  isochronous 
pendulum  measure  its  smaller  portions.  By  these  in- 
variable standards  alone  we  can  judge  of  the  slow 
changes  that  other  elements  of  the  system  may  have 
undergone.  Apparent  sidereal  time,  which  is  measured 
by  the  transit  of  the  equinoctial  point  at  the  meridian  of 
any  place,  is  a  variable  quantity,  from  the  effects  of 
precession  and  nutation.  Clocks  showing  apparent 
sidereal  time  are  employed  for  observation,  and  are  so 
regulated  that  they  indicate  Oh  Om  0s  at  the  instant  the 
equinoctial  point  passes  the  meridian  of  the  observatory. 
And  as  time  is  a  measure  of  angular  motion,  the  clock 
gives  the  distances  of  the  heavenly  bodies  from  the 
equinox  by  observing  the  instant  at  which  each  passes 
the  meridian,  and  converting  the  interval  into  arcs  at  the 
rate  of  15°  to  an  hour. 

The  returns  of  the  sun  to  the  meridian  and  to  the 
same  equinox  or  solstice,  have  been  universally  adopted 
as  the  measure  of  our  civil  days  and  years.  The  solar 
or  astronomical  day  is  the  time  that  elapses  between 
two  consecutive  noons  or  midnights.  It  is  consequently 
longer  than  the  sidereal  day,  on  account  of  the  proper 
motion  of  the  sun  during  a  revolution  of  the  celestial 
sphere.  But  as  the  sun  moves  with  greater  rapidity  at 
the  winter  than  at  the  summer  solstice,  the  astronomi- 
cal day  is  more  nearly  equal  to  the  sidereal  day  in  sum- 
mer than  in  winter.  The  obliquity  of  the  ecliptic  also 
affects  its  duration ;  for  near  the  equinoxes  the  arc  of 
the  equator  is  less  than  the  corresponding  arc  of  the 
ecliptic,  and  in  the  solstices  it  is  greater  (N.  145).  The 
astronomical  day  is  therefore  diminished  in  the  first 
case,  and  increased  in  the  second.  If  the  sun  moved 
uniformly  in  the  equator  at  the  rate  of  59'  8"- 33  every 
day,  the  solar  days  would  be  all  equal.  The  time  there- 
fore which  is  reckoned  by  the  arrival  of  an  imaginary 
sun  at  the  meridian,  or  of  one  which  is  supposed  to 
move  uniformly  in  the  equator,  is  denominated  mean 
solar  time,  such  as  is  given  by  clocks  and  watches  in 
common  life.  When  it  is  reckoned  by  the  arrival  of  the 
real  sun  at  the  meridian  it  is  apparent  time,  such  as  is 
given  by  dials.  The  difference  between  the  time  shown 
by  a  clock  and  a  dial  is  the  equation  of  time  given  in 


SICT.  XII.  DIVISIONS  OF  TIME.  79 

the  Nautical  Almanac,  sometimes  amounting  to  as  much 
as  sixteen  minutes.  The  apparent  and  mean  time  coin- 
cide four  times  in  the  year ;  when  the  sun's  daily  mo- 
tion in  right  ascension  is  equal  to  59'  &"•  33  in  a  mean 
solar  day,  which  happens  about  the  16th  of  April,  the 
16th  of  June,  the  1st  of  September,  and  the  25th  of 
December. 

The  astronomical  day  begins  at  noon,  but  in  common 
reckoning  the  day  begins  at  midnight.  In  England  it  is 
divided  into  twenty-four  hours,  which  are  counted  by 
twelve  and  twelve  ;  but  in  France  astronomers,  adopting 
the  decimal  division,  divide  the  day  into  ten  hours,  the 
hour  into  one  hundred  minutes,  and  the  minute  into  a 
hundred  seconds,  because  of  the  facility  in  computation, 
and  in  conformity  with  then*  decimal  system  of  weights 
and  measures.  This  subdivision  is  not  now  used  in 
common  life,  nor  has  it  been  adopted  in  any  other 
country  ;  and  although  some  scientific  writers  in  France 
still  employ  that  division  of  time,  the  custom  is  begin- 
ning to  wear  out.  At  one  period  during  the  French 
revolution,  the  clock  in  the  gardens  of  the  Tuileries  was 
regulated  to  show  decimal  time.  The  mean  length  of 
the  day,  though  accurately  determined,  is  not  sufficient 
for  the  purposes  either  of  astronomy  or  civil  life.  The 
tropical  or  civil  year  of  365d  5U  48m  498-7,  which  is  the 
time  elapsed  between  the  consecutive  returns  of  the«un 
to  the  mean  equinoxes  or  solstices,  including  all  the 
changes  of  the  seasons,  is  a  natural  cycle  peculiarly 
suited  for  a  measure  of  duration.  It  is  estimated  from 
the  winter  solstice,  the  middle  of  the  long  annual  night 
under  the  north  pole.  But  although  the  length  of  the 
civil  year  is  pointed  out  by  nature  as  a  measure  of  long 
periods,  the  incommensurability  that  exists  between  the 
length  of  the  day  and  the  revolution  of  the  sun,  renders 
it  difficult  to  adjust  the  estimation  of  both  in  whole  num- 
bers. If  the  revolution  of  the  sun  were  accomplished 
in  365  days,  all  the  years  would  be  of  precisely  the  same 
number  of  days,  and  would  begin  and  end  with  the  sun 
at  the  same  point  of  the  ecliptic.  But  as  the  sun's  revo- 
lution includes  the  fraction  of  a  day,  a  civil  year  and  a 
revolution  of  the  sun  have  not  the  same  duration.  Since 
the  fraction  is  nearly  the  fourth  of  a  day,  in  four  years 


80  LENGTH  OF  THE  CIVIL  YEAR.  SECT.  XII. 

it  is  nearly  equal  to  a  revolution  of  the  sun,  so  that  the 
addition  of  a  supernumerary  day  every  fourth  year 
nearly  compensates  the  difference.  But  in  process  of 
time  further  correction  will  be  necessary,  because  the 
fraction  is  less  than  the  fourth  of  a  day.  In  fact,  if  a 
bissextile  be  suppressed  at  the  end  of  three  out  of  four 
centuries,  the  year  so  determined  will  only  exceed  the 
true  year  by  an  extremely  small  fraction  of  a  day  ;  and 
if  in  addition  to  this  a  bissextile  be  suppressed  every 
4000  years,  the  length  of  the  year  will  be  nearly  equal 
to  that  given  by  observation.  Were  the  fraction  neg- 
lected, the  beginning  of  the  year  would  precede  that  of 
the  tropical  year,  so  that  it  would  retrograde  through 
the  different  seasons  in  a  period  of  about  1507  years. 
The  Egyptian  year  began  with  the  heliacal  rising  of 
Sirius,  and  contained  only  365  days,  by  which  they  lost 
one  year  in  every  1461  years,  their  Sothaic  period,  or  that 
cycle  in  which  the  heliacal  rising  of  Sirius  passes  through 
the  whole  year  and  takes  place  again  on  the  same  day. 
The  commencement  of  that  cycle  is  placed  by  ancient 
chronologists  in  the  year  1322  before  the  Christian  era. 
The  division  of  the  year  into  months  is  very  old  and  almost 
universal.  But  the  period  of  seven  days,  by  far  the 
most  permanent  division  of  time,  and  the  most  ancient 
monument  of  astronomical  knowledge,  was  used  by  the 
Brahmins  in  India  with  the  same  denominations  em- 
ployed by  us,  and  was  alike  found  in  the  calendars  of  the 
Jews,  Egyptians,  Arabs,  and  Assyrians.  It  has  survived 
the  fall  of  empires,  and  has  existed  among  all  successive 
generations,  a  proof  of  their  common  origin. 

The  day  of  the  new  moon  immediately  following  the 
winter  solstice  in  the  707th  year  of  Rome,  was  made  the 
1st  of  January  of  the  first  year  of  Julius  Caesar.  The 
25th  of  December  of  his  forty-fifth  year  is  considered  as 
the  date  of  Christ's  nativity ;  and  the  forty-sixth  year  of 
the  Julian  Calendar  is  assumed  to  be  the  first  of  our 
era.  The  preceding  year  is  called  the  first  year  before 
Christ  by  chronologists,  but  by  astronomers  it  is  called 
the  year  0.  The  astronomical  year  begins  on  the  31st 
of  December  at  noon ;  and  the  date  of  an  observation 
expresses  the  days  and  hours  which  have  actually  elapsed 
since  that  time. 


S«CT.  XII.  ASTRONOMICAL  ERAS.  81 

.  Since  solar  and  sidereal  time  are  estimated  from  the 
passage  of  the  sun  and  the  equinoctial  point  across  the 
meridian  of  each  place,  the  hours  are  different  at  differ- 
ent places :  while  it  is  one  o'clock  at  one  place  it  is  two 
at  another,  three  at  another,  &c. ;  for  it*  is  obvious  that 
it  is  noon  at  one  part  of  the  globe,  at  the  same  moment 
that  it  is  midnight  at  another  diametrically  opposite  to  it; 
consequently  an  event  which  happens  at  one  and  the 
same  instant  of  absolute  time  is  recorded  at  different 
places,  as  having  happened  at  different  times.  There- 
fore, when  observations  made  at  different  places  are  to 
be  compared,  they  must  be  reduced  by  computation  to 
what  they  would  have  been  had  they  been  made  under 
the  same  meridian.  To  obviate  this,  it  was  proposed  by 
Sir  John  Herschel  to  employ  mean  equinoctial  time, 
which  is  the  same  for  all  the  world,  and  independent 
alike  of  local  circumstances  and  inequalities  in  the  sun's 
motion.  It  is  the  time  elapsed  from  the  instant  the  mean 
sun  enters  the  mean  vernal  equinox,  and  is  reckoned  in 
mean  solar  days  and  parts  of  a  day. 

Some  remarkable  astronomical  eras  are  determined  by 
the  position  of  the  major  axis  of  the  solar  ellipse,  which 
depends  upon  the  direct  motion  of  the  perigee  (N.  102) 
and  the  precession  of  the  equinoxes  conjointly,  the 
annual  motion  of  the  one  being  ]1"*8,  and  that  of  the 
other  50"-1.  Hence  the  axis,  moving  at  the  rate  of 
61"-9  annually,  accomplishes  a  tropical  revolution  in 
209-84  years.  It  coincided  with  the  line  of  the  equinoxes 
4000  or  4089  years  before  the  Christian  era,  much  about 
the  time  chronologists  assign  for  the  creation  of  man.  In 
6483  the  major  axis  will  again  coincide  with  the  line  of 
the  equinoxes ;  but  then  the  solar  perigee  will  coincide 
with  the  equinox  of  autumn  ;  whereas  at  the  creation  of 
man  it  coincided  with  the  vernal  equinox.  In  the  year 
1246  the  major  axis  was  perpendicular  to  the  line  of  the 
equinoxes  ;  then  the  solar  perigee  coincided  with  the 
solstice  of  summer,  and  the  apogee  with  the  solstice  of 
winter.  According  to  La  Place,  who  computed  these 
periods  from  different  data,  the  last  coincidence  hap- 
pened in  the  year  1250  of  our  era,  which  induced  him  to 
propose  that  year  as  a  universal  epoch,  the  vernal  equi- 
nox of  the  year  1250  to  be  the  first  day  of  the  first  year. 
6 


82  ANCIENT  CHRONOLOGY.  SECT.  XII 

These  eras  can  only  be  regarded  as  approximate,  since 
ancient  observations  are  too  inaccurate,  and  modern  ob- 
servations too  recent,  to  afford  data  for  their  precise 
determination. 

The  variation  in  the  position  of  the  solar  ellipse  occa- 
sions corresponding  changes  in  the  length  of  the  seasons. 
In  its  present  position  spring  is  shorter  than  summer, 
and  autumn  longer  than  winter ;  and  while  the  solar 
perigee  continues  as  it  now  is  between  the  solstice  of 
winter  and  the  equinox  of  spring,  the  period  including 
spring  and  summer  will  be  longer  than  that  including 
autumn  and  winter.  In  this  century  the  difference  is 
between  seven  and  eight  days.  The  intervals  will  be 
equal  toward  the  year  6483,  when  the  perigee  will  coin- 
cide with  the  equinox  of  spring  ;  but  when  it  passes  that 
point,  the  spring  and  summer  taken  together  will  be 
shorter  than  the  period  including  the  autumn  and  winter 
(N.  147).  These  changes  will  be  accomplished  in  a 
tropical  revolution  of  the  major  axis  of  the  earth's  orbit, 
which  includes  an  interval  of  20,984  years.  Were  the 
orbit  circular,  the  seasons  would  be  equal ;  their  differ- 
ence arises  from  the  eccentricity  of  the  orbit,  small  as  it 
is  ;  but  the  changes  are  so  trifling  as  to  be  imperceptible 
in  the  short  span  of  human  life. 

No  circumstance  in  the  whole  science  of  astronomy 
excites  a  deeper  interest  than  its  application  to  chronol- 
ogy. "Whole  nations,"  says  La  Place,  "have  been 
swept  from  the  earth,  with  their  languages,  arts,  and 
sciences,  leaving  but  confused  masses  of  ruins  to  mark 
the  place  where  mighty  cities  stood  ;  their  history  with 
the  exception  of  a  few  doubtful  traditions  has  perished  ; 
but  the  perfection  of  their  astronomical  observations 
marks  their  high  antiquity,  fixes  the  periods  of  their  ex- 
istence, and  proves  that  even  at  that  early  time  they 
must  have  made  considerable  progress  in  science."  The 
ancient  state  of  the  heavens  may  now  be  computed  with 
great  accuracy  ;  and  by  comparing  the  results  of  calcu- 
lation with  ancient  observations,  the  exact  period  at 
which  they  were  made  may  be  verified  if  true,  or  if 
false  their  error  may  be  detected.  If  the  date  be  accu- 
rate and  the  observation  good,  it  will  verify  the  accuracy 
of  modern  tables,  and  will  show  to  how  many  centuries 


SECT.  XII.  ANCIRNT  ASTRONOMY.  83 

they  may  be  extended  without  the  fear  of  error.     A  few 
examples  will  show  the  importance  of  the  subject. 

At  the  solstices  the  sun  is  at  his  greatest  distance  from 
the  equator,  consequently  his  declination  at  these  times 
is  equal  to  the  obliquity  of  the  ecliptic  (N.  148),  which 
was  formerly  determined  from  the  meridian  length  of 
the  shadow  of  the  stile  of  a  dial  on  the  day  of  a  solstice. 
The  lengths  of  the  meridian  shadow  at  the  summer  and 
winter  solstices  are  recorded  to  have  been  observed  at 
the  city  of  Layang,  in  China,  1100  years  before  the 
Christian  era.  From  these  the  distances  of  the  sun 
from  the  zenith  (N.  149)  of  the  city  of  Layang  are 
known.  Half  the  sum  of  these  zenith  distances  de- 
termines the  latitude,  and  half  their  difference  gives  the 
obliquity  of  the  ecliptic  at  the  period  of  the  observation  ; 
and  as  the  law  of  the  variation  of  the  obliquiryis  known, 
both  the  time  and  place  of  the  observations  have  been 
verified  by  computations  from  modern  tables.  Thus 
the  Chinese  had  made  some  advances  in  the  science  of 
astronomy  at  that  early  period.  Their  whole  chronol- 
ogy is  founded  on  the  observations  of  eclipses,  which 
prove  the  existence  of  that  empire  for  more  than  4700 
years.  The  epoch  of  the  lunar  tables  of  the  Indians, 
supposed  by  Bailly  to  be  3000  years  before  the  Chris- 
tian era,  was  proved  by  La  Place,  from  the  acceleration 
of  the  moon,  not  to  be  more  ancient  than  the  time  of 
Ptolemy,  who  lived  in  the  second  century  after  it.  The 
great  inequality  of  Jupiter  and  Saturn,  whose  cycle  em- 
braces 918  years,  is  peculiarly  fitted  for  marking  the 
civilization  of  a  people.  The  Indians  had  determined 
the  mean  motions  of  these  two  planets  in  that  part  of 
their  periods,  when  the  apparent  mean  motion  of  Saturn 
was  at  the  slowest,  and  that  of  Jupiter  the  most  rapid. 
The  periods  in  which  that  happened  were  3102  years 
before  the  Christian  era,  and  the  year  1491  after  it. 
The  returns  of  comets  to  their  perihelia  may  possibly 
mark  the  present  state  of  astronomy  to  future  ages. 

The  places  of  the  fixed  stars  are  affected  by  the  pre- 
cession of  the  equinoxes ;  and  as  the  law  of  that  varia- 
tion is  known,  their  positions  at  any  time  may  be  com- 
puted. Now  Eudoxus,  a  contemporary  of  Plato,  men- 
tions a  star  situate  in  the  pole  of  the  equator,  and  it  ap- 


84  WEIGHTS  AND  MEASURES.  SECT.  XII. 

pears  from  computation  that  K  Draconis  was  not  very 
far  from  that  place  about  3000  years  ago  ;  but  as- it  is 
only  about  2150  years  since  Eudoxus  lived,  he  must 
have  described  an  anterior  state  of  the  heavens,  sup- 
posed to  be  the  same  that  was  mentioned  by  Chiron 
about  the  time  of  the  siege  of  Troy.  Thus  every  cir- 
cumstance concurs  in  showing  that  astronomy  was  cul- 
tivated in  the  highest  ages  of  antiquity. 

It  is  possible  that  a  knowledge  of  astronomy  may  lead 
to  the  interpretation  of  hieroglyphical  characters.  As- 
tronomical signs  are  often  found  on  the  ancient  Egyptian 
monuments,  probably  employed  by  the  priests  to  record 
dates.  The  author  had  occasion  to  witness  an  instance 
of  this  most  interesting  application  of  astronomy,  in  as- 
certaining the  date  of  a  papyrus,  sent  from  Egypt  by  Mr. 
Salt,  in  the  hieroglyphical  researches  of  the  late  Dr. 
Thomas  Young,  whose  profound  and  varied  acquire- 
ments do  honor  to  his  country,  and  to  the  age  in  which 
he  lived.  The  manuscript  was  found  in  a  mummy  case  ; 
it  proved  to  be  a  horoscope  of  the  age  of  Ptolemy,  and 
its  date  was  determined  from  the  configuration  of  the 
heavens  at  the  time  of  its  construction. 

The  form  of  the  earth  furnishes  a  standard  of  weights 
and  measures  for  the  ordinary  purposes  of  life,  as  well 
as  for  the  determination  of  the  masses  and  distances  of 
the  heavenly  bodies.  The  length  of  the  pendulum 
vibrating  seconds  of  mean  solar  time  in  the  latitude  of 
London,  forms  the  standard  of  the  British  measure  of 
extension.  Its  approximate  length  oscillating  in  vacuo 
at  the  temperature  of  62°  of  Fahrenheit,  and  reduced 
to  the  level  of  the  sea  (N.  150),  was  determined  by 
Captain  Kater  to  be  39-1393  inches.  The  weight  of  a 
cubic  inch  of  water  at  the  temperature  of  62°  of 
Fahrenheit,  barometer  30  inches,  was  also  determined 
in  parts  of  the  imperial  troy  pound,  whence  a  standard 
both  of  weight  and  capacity  was  deduced.  The  French 
have  adopted  the  metre  equal  to  3-2808992  English  feet 
for  their  unit  of  linear  measure,  which  is  the  ten-mil- 
lionth part  of  that  quadrant  of  the  meridian  (N.  151), 
passing  through  Formentera  and  Greenwich,  the  middle 
of  which  is  nearly  in  the  forty-fifth  degree  of  latitude. 
Should  the  national  standards  of  the  two  countries  be 


S«cr  X1H.  WEIGHTS  AND  MEASURES  85 

lost  in  the  vicissitude  of  human  affairs,  both  may  be 
recovered  ;  since  they  are  derived  from  natural  standards 
presumed  to  be  invariable.  The  length  of  the  pendu- 
lum would  be  found  again  with  more  facility  than  the 
metre.  But  as  no  measure  is  mathematically  exact,  an 
error  in  the  original  standard  may  at  length  become 
sensible  in  measuring  a  great  extent,  whereas  the  error 
that  must  necessarily  arise  in  measuring  the  quadrant  of 
the  meridian  is  rendered  totally  insensible  by  subdi- 
vision in  taking  its  ten-millionth  part.  The  French 
have  adopted  the  decimal  division,  not  only  in  time  but 
also  in  their  degrees,  weights,  and  measures,  on  account 
of  the  very  great  facility  it  affords  in  computation.  It 
has  not  been  adopted  by  any  other  people,  though 
nothing  is  more  desirable  than  that  all  nations  should 
concur  in  using  the  same  standards,  not  only  on  account 
of  convenience,  but  as  affording  a  more  definite  idea  of 
quantity.  It  is  singular  that  the  decimal  division  of  the 
day,  of  degrees,  weights,  and  measures,  was  employed 
in  China  4000  years  ago ;  and  that  at  the  time  Ibn  Tunis 
made  his  observations  at  Cairo  about  the  year  1000  of 
the  Christian  era,  the  Arabs  were  in  the  habit  of  em- 
ploying the  vibrations  of  the  pendulum  in  their  astro- 
nomical observations  as  a  measure  of  time. 


SECTION  XIII. 

Tides — Forces  that  produce  them — Three  kinds  of  Oscillations  in  the  Ocean 
—The  Semidiurnal  Tides— Equinoctial  Tides— Effects  of  the  Declina- 
tion of  the  Sun  and  Moon — Theory  insufficient  without  Observation — 
Direction  of  the  Tidal  Wave — Height  of  Tides — Mass  of  Moon  obtained 
from  her  Action  on  the  Tides — Interference  of  Undulations — Impossi- 
bility of  a  Universal  Inundation — Currents. 

ONE  of  the  most  immediate  and  remarkable  effects  of 
a  gravitating  force  external  to  the  earth,  is  the  alternate 
rise  and  fall  of  the  surface  of  the  sea  twice  in  the  course 
of  a  lunar  day,  or  24h  50m  28s  of  mean  solar  time.  As  it 
depends  upon  the  action  ofthe  sun  and  moon,  it  is  classed 
among  astronomical  problems,  of  which  it  is  by  far  the 
most  difficult  and  its  explanation  the  least  satisfactory. 
The  form  of  the  surface  of  the  ocean  in  equilibrio  when 
revolving  with  the  earth  round  its  axis,  is  an  ellipsoid 
H 


86  THEORY  OF  THE  TIDES.  SKCT.  XIH. 

flattened  at  the  poles  ;  but  the  action  of  the  sun  and 
moon,  especially  of  the  moon,  disturbs  the  equilibrium  of 
the  ocean.  If  the  moon  attracted  the  center  of  gravity 
of  the  earth  and  all  its  particles  with  equal  and  parallel 
forces,  the  whole  system  of  the  earth  and  the  waters 
that  cover  it  would  yield  to  these  forces  with  a  common 
motion,  and  the  equilibrium  of  the  seas  would  remain 
undisturbed.  The  difference  of  the  forces  and  the  ine- 
quality of  their  directions  alone  disturb  the  equilibrium. 

It  is  proved  by  daily  experience  as  well  as  by  strict 
mathematical  reasoning,  that  if  a  number  of  waves  or 
oscillations  be  excited  in  a  fluid  by  different  forces,  each 
pursues  its  course  and  has  its  effect  independently  of 
the  rest.  Now  in  the  tides  there  are  three  kinds  of 
oscillations  depending  on  different  causes,  and  producing 
their  effects  independently  of  each  other,  which  may 
therefore  be  estimated  separately. 

The  oscillations  of  the  first  kind,  which  are  very  small, 
are  independent  of  the  rotation  of  the  earth  ;  and  as  they 
depend  upon  the  motion  of  the  disturbing  body  in  its 
orbit,  they  are  of  long  periods.  The  second  kind  of 
oscillations  depends  upon  the  rotation  of  the  earth, 
therefore  their  period  is  nearly  a  day.  The  oscillations 
of  the  third  kind  vary  with  an  angle  equal  to  twice  the 
angular  rotation  of  the  earth,  and  consequently  happen 
twice  in  twenty-four  hours  (N.  152).  The  first  afford 
no  particular  interest,  and  are  extremely  small ;  but  the 
difference  of  two  consecutive  tides  depends  upon  the 
second.  At  the  time  of  the  solstices,  this  difference, 
which  ought  to  be  very  great  according  to  Newton's 
theory,  is  hardly  sensible  on  our  shores.  La  Place  has 
shown  that  the  discrepancy  arises  from  the  depth  of  the 
sea ;  and  that  if  the  depth  were  uniform,  there  would 
be  no  difference  in  the  consecutive  tides  but  that  which 
is  occasioned  by  local  circumstances.  It  follows  there- 
fore that  as  this  difference  is  extremely  small,  the  sea 
considered  in  a  large  extent  must  be  nearly  of  uniform 
depth  ;  that  is  to  say,  there  is  a  certain  mean  depth  from 
which  the  deviation  is  not  great.  The  mean  depth  of 
the  Pacific  Ocean  is  supposed  to  be  about  four  or  five 
miles,  that  of  the  Atlantic  only  three  or  four,  which, 
however,  is  mere  conjecture.  From  the  formula3,  which 


SBCT.  XIII.  THEORY  OF  THE  TIDES.  87 

determine  the  difference  of  the  consecutive  tides,  it  is 
proved  that  the  precession  of  the  equinoxes,  and  the 
nutation  of  the  earth's  axis,  are  the  same  as  if  the  sea 
formed  one  solid  mass  with  the  earth. 

Oscillations  of  the  third  kind  are  the  semidiurnal  tides 
so  remarkable  on  our  coasts.  They  are  occasioned  by 
the  combined  action  of  the  sun  and  moon ;  but  as  the 
effect  of  each  is  independent  of  the  other,  they  may  be 
considered  separately. 

The  particles  of  water  under  the  moon  are  more  at- 
tracted than  the  center  of  gravity  of  the  earth,  in  the 
inverse  ratio  of  the  square  of  the  distances.  Hence 
they  have  a  tendency  to  leave  the  earth,  but  are  retained 
by  their  gravitation,  which  is  diminished  by  this  tendency. 
On  the  contrary,  the  moon  attracts  the  center  of  the 
earth,  more  powerfully  than  she  attracts  the  particles  of 
water  in  the  hemisphere  opposite  to  her ;  so  that  the 
earth  has  a  tendency  to  leave  the  waters,  but  is  retained 
by  gravitation,  which  is  again  diminished  by  this  tendency. 
Thus  the  waters  immediately  under  the  moon  are  drawn 
from  the  earth,  at  the  same  time  that  the  earth  is  drawn 
from  those  which  are  diametrically  opposite  to  her,  in 
both  instances  producing  an  elevation  of  the  ocean  of 
nearly  the  same  height  above  the  surface  of  equilibrium; 
for  the  diminution  of  the  gravitation  of  the  particles  in 
each  position  is  almost  the  same,  on  account  of  the  dis- 
tance of  the  moon  being  great  in  comparison  of  the  ra- 
dius of'the  earth.  Were  the  earth  entirely  covered  by 
the  sea,  the  waters  thus  attracted  by  the  moon  would 
assume  the  form  of  an  oblong  spheroid  whose  greater 
axis  would  point  toward  the  moon  ;  since  the  columns  of 
water  under  the  moon,  and  in  the  direction  diametrically 
opposite  to  her,  are  rendered  lighter  in  consequence  of 
the  diminution  of  their  gravitation ;  and  in  order  to  pre- 
serve the  equilibrium,  the  axes  90°  distant  would  be 
shortened.  The  elevation,  on  account  of  the  smaller 
space  to  which  it  is  confined,  is  twice  as  great  as  the 
depression  ;  because  the  contents  of  the  spheroid  always 
remain  the  same.  If  the  waters  were  capable  of  assum- 
ing the  form  of  equilibrium  instantaneously,  that  is  the 
form  of  the  spheroid,  its  summit  would  always  point  to 
the.inoon  notwithstanding  the  earth's  rotation.  But  on 


88  THE  SEMIDIURNAL  TIDES.  SECT.  XIII. 

account  of  their  resistance,  the  rapid  motion  produced 
in  them  by  rotation  prevents  them  from  assuming  at 
every  instant  the  form  which  the  equilibrium  of  the 
forces  acting  upon  them  requires.  Hence  on  account 
of  the  inertia  of  the  waters,  if  the  tides  be  considered 
relatively  to  the  whole  earth  and  open  seas,  there  is  a 
meridian  about  30°  eastward  of  the  moon,  where  it  is 
always  high  water  both  in  the  hemisphere  where  the 
moon  is  and  in  that  which  is  opposite.  On  the  west 
side  of  this  circle  the  tide  is  flowing,  on  the  east  it  is 
ebbing,  and  on  every  part  of  the  meridian  at  90°  distant 
it  is  low  water.  This  great  wave,  which  follows  all  the 
motions  of  the  moon  as  far  as  the  rotation  of  the  earth 
will  permit,  is  modified  by  the  action  of  the  sun,  the 
effects  of  whose  attraction  are  in  every  respect  like 
those  produced  by  theJmoon,  though  greatly  less  in  de- 
gree. Consequently  a  similar  wave,  but  much  smaller, 
raised  by  the  sun  tends  to  follow  his  motions,  which  at 
times  combines  with  the  lunar  wave,  and  at  others  op- 
poses it,  according  to  the  relative  positions  of  the  two 
luminaries ;  but  as  the  lunar  wave  is  only  modified  a 
little  by  the  solar,  the  tides  must  necessarily  happen 
twice  in  a  day,  since  the  rotation  of  the  earth  brings  the 
same  point  twice  under  the  meridian  of  the  moon  in 
that  time,  once  under  the  superior  and  once  under  the 
inferior  meridian. 

In  the  semidiurnal  tides  there  are  two  phenomena 
particularly  to  be  distinguished,  one  occurring  twice  in  a 
month,  and  the  other  twice  in  a  year. 

The  first  phenomenon  is  that  the  tides  are  much  in- 
creased in  the  syzygies,  or  at  the  time  of  new  and  full 
moon  (N.  153).  In  both  cases  the  sun  and  moon  are  in 
the  same  meridian  :  for  when  the  moon  is  new  they  are 
in  conjunction  ;  and  when  she  is  full  they  are  in  opposi- 
tion. In  each  of  these  positions,  their  action  is  com- 
bined to  produce  the  highest  or  spring  tides  under  that 
meridian,  and  the  lowest  in  those  points  that  are  90° 
distant.  It  is  observed  that  the  higher  the  sea  rises  in 
full  tide,  the  lower  it  is  in  the  ebb.  The  neap  tides  take 
place  when  the  moon  is  in  quadrature  ;  they  neither  rise 
so  high  nor  sink  so  low  as  the  spring  tides.  The  spring 
tides  are  much  increased  when  the  moon  is  in  perigee, 


S«CT.  Xffl.  SPRING  AND  NEAP  TIDES.  89 

because  she  is  then  nearest  to  the  earth.  It  is  evident 
that  the  strong  tides  must  happen  twice  in  a  month, 
since  in  that  time  the  moon  is  once  new  and  once  full. 

The  second  phenomenon  in  the  tides  is  the  augmen- 
tation occurring  at  the  time  of  the  equinoxes  when  the 
sun's  declination  (N.  154)  is  zero,  which  happens  twice 
every  year.  The  greatest  tides  take  place  when  a  new 
or  full  moon  happens  near  the  equinoxes,  while  the 
moon  is  in  perigee.  The  inclination  of  the  moon's  orbit 
to  the  ecliptic  is  5°  8'  47"-9;  hence  in  the  equinoxes  the 
action  of  the  moon  would  be  increased  if  her  node  were 
to  coincide  with  her  perigee ;  for  it  is  clear  that  the  ac- 
tion of  the  sun  and  moon  on  the  ocean  is  most  direct 
and  intense  when  they  are  in  the  plane  of  the  equator, 
and  in  the  same  meridian,  and  when  the  moon  in  con- 
junction or  opposition  is  at  her  least  distance  from  the 
earth.  The  spring  tides  which  happen  under  all  these 
favorable  circumstances  must  be  the  greatest  possible. 
The  equinoctial  gales  often  raise  them  to  a  great  height. 
Besides  these  remarkable  variations,  there  are  others 
arising  from  the  declination  or  angular  distance  of  the 
sun  and  moon  from  the  plane  of  the  equator,  which  have 
a  great  influence  on  the  ebb  and  flow  of  the  waters.  The 
sun  and  moon  are  continually  making  the  circuit  of  the 
heavens  at  different  distances  from  the  plane  of  the 
equator,  on  account  of  the  obliquity  of  the  ecliptic  and 
the  inclination  of  the  lunar  orbit.  The  moon  takes  about 
twenty-nine  days  and  a  half  to  vary  through  all  her  de- 
clinations, which  sometimes  extend  28|  degrees  on  each 
side  of  the  equator,  while  the  sun  requires  nearly  365| 
days  to  accomplish  his  motion  from  tropic  to  tropic 
through  about  23^  degrees ;  so  that  their  combined  mo- 
tion causes  great  irregularities,  and  at  times  their  at- 
tractive forces  counteract  each  other's  effects  to  a  certain 
extent ;  but  on  an  average  the  mean  monthly  range  of 
the  moon's  declination  is  nearly  the  same  as  the  annual 
range  of  the  declination  of  the  sun :  consequently  the 
highest  tides  take  place  within  the  tropics,  and  the  low- 
est toward  the  poles.  The  declination  of  the  moon 
likewise  causes  the  two  tides  of  the  same  day  to  rise  to 
unequal  heights ;  this  diurnal  inequality  of  course  van- 
ishes when  the  moon  is  in  the  equator. 
H2 


90  THEORY  OP  THE  TIDES.  SECT.  XIII. 

Both  the  height  and  time  of  high  water  are  thus  per- 
petually changing ;  therefore,  in  solving  the  problem,  it 
is  required  to  determine  the  heights  to  which  the  tides 
rise,  the  times  at  which  they  happen,  and  the  daily  vari- 
ations. Theory  and  observation  show  that  each  partial 
tide  increases  as  the  cube  of  the  apparent  diameter,  or 
of  the  parallax  of  the  body  which  produces  it,  and  that  it 
diminishes  as  the  square  of  the  cosine  of  the  declination 
of  that  body  (N.  154) ;  for  the  greater  the  apparent  di- 
ameter, the  nearer  the  body,  and  the  more  intense  its 
action  on  the  sea;  but  the  greater  the  decimation,  the 
less  the  action,  because  it  is  less  direct. 

The  periodic  motions  of  the  waters  of  the  ocean,  on 
the  hypothesis  of  an  ellipsoid  of  revolution  entirely  cov- 
ered by  the  sea,  are  very  far  from  according  with  obser- 
vation. This  arises  from  the  very  great  irregularities  in 
the  surface  of  the  earth,  which  is  but  partially  covered 
by  the  sea  ;  from  the  variety  in  the  depths  of  the  ocean, 
the  manner  in  which  it  is  spread  out  on  the  earth,  the 
position  and  inclination  of  the  shores,  the  currents,  and 
the  resistance  the  waters  meet  with — causes  impossible 
to  estimate,  but  which  modify  the  oscillations  of  the 
great  mass  of  the  ocean.  However,  amid  all  these 
irregularities,  the  ebb  and  flow  of  the  sea  maintain  a 
ratio  to  the  forces  producing  them  sufficient  to  indicate 
their  nature  and  to  verify  the  law  of  the  attraction  of  the 
sun  and  moon  on  the  sea.  La  Place  observes  that  the 
investigation  of  such  relations  between  cause  and  effect 
is  no  less  useful  in  natural  philosophy  than  the  direct 
solution  of  problems  either  to  prove  the  existence  of  the 
causes  or  to  trace  the  laws  of  their  effects.  Like  the 
theory  of  probabilities,  it  is  a  happy  supplement  to  the 
ignorance  and  weakness  of  the  human  mind.  Thus 
the  problem  of  the  tides  does  not  admit  of  a  general 
solution.  It  is,  indeed,  necessary  to  analyze  the  general 
phenomena  which  ought  to  result  from  the  attraction  of 
the  sun  and  moon ;  but  these  must  be  corrected  in  each 
particular  case  by  local  observations  modified  by  the 
extent  and  depth  of  the  sea,  and  the  peculiar  circum- 
stances of  the  place. 

Since  the  disturbing  action  of  the  sun  and  moon  can 
only  become  sensible  in  a  very  great  extent  of  water, 


S«cr.  XIII.  HEIGHT  OF  THE  TIDES.  91 

the  Pacific  Ocean  must  be  one  of  the  principal  sources 
of  our  tides  ;  but,  in  consequence  of  the  rotation  of  the 
earth  and  the  inertia  of  the  ocean,  high  water  does  not 
happen  till  some  time  after  the  moon's  southing  (N.  155). 
The  tide  raised  in  that  world  of  waters  is  transmitted  to 
the  Atlantic,  from  which  sea  it  moves  in  a  northerly 
direction  along  the  coasts  of  Africa  and  Europe,  arriving 
later  and  later  at  each  place.  This  great  wave,  how- 
ever, is  modified  by  the  tide  raised  in  the  Atlantic, 
which  sometimes  combines  with  that  from  the  Pacific 
in  raising  the  sea,  and  sometimes  is  in  opposition  to  it, 
so  that  the  tides  only  rise  in  proportion  to  their  differ- 
ence. This  vast  combined  wave,  reflected  by  the  shores 
of  the  Atlantic,  extending  nearly  from  pole  to  pole,  still 
coming  northward,  pours  through  the  Irish  and  British 
Channels  into  the  North  Sea ;  so  that  the  tides  in  our 
ports  are  modified  by  those  of  another  hemisphere. 
Thus  the  theory  of  the  t&ies  in  each  port,  both  as  to  their 
height  and  the  times  at  which  they  take  place,  is  really 
a  matter  of  experiment,  and  can  only  be  perfectly  deter- 
mined by  the  mean  of  a  very  great  number  of  observa- 
tions, including  several  revolutions  of  the  moon's  nodes. 
The  height  to  which  the  tides  rise  is  much  greater  in 
narrow  channels  than  in  the  open  sea,  on  account  of  the 
obstructions  they  meet  with.  The  sea  is  so  pent  up  in 
the  British  Channel  that  the  tides  sometimes  rise  as 
much  as  fifty  feet  at  St.  Malo  on  the  coast  of  France ; 
whereas  on  the  shores  of  some  of  the  South  Sea  islands 
near  the  center  of  the  Pacific  they  do  not  exceed  one 
or  two  feet.  The  winds  have  great  influence  on  the 
height  of  the  tides,  according  as  they  conspire  with  or 
oppose  them ;  but  the  actual  effect  of  the  wind  in  ex- 
citing the  waves  of  the  ocean  extends  very  little  below 
the  surface.  Even  in  the  most  violent  storms,  the  water 
is  probably  calm  at  the  depth  of  ninety  or  a  hundred 
feet.  The  tidal  wave  of  the  ocean  does  not  reach  the 
Mediterranean  nor  the  Baltic,  partly  from  their  position 
and  partly  from  the  narrowness  of  the  Straits  of  Gib- 
raltar and  of  the  Categat,  but  it  is  very  perceptible  in 
the  Red  Sea  and  in  Hudson's  Bay.  In  high  latitudes, 
where  the  ocean  is  less  directly  under  the  influence  of 
the  luminaries,  the  rise  and  fall  of  the  sea  w  inconsider- 


92  ACTION  OP  SUN  AND  MOON.  SECT.  XIII. 

able,  so  that  in  all  probability  there  is  no  tide  at  the 
poles,  or  only  a  small  annual  and  monthly  tide.  The 
ebb  and  flow  of  the  sea  are  perceptible  in  rivers  to  a 
very  great  distance  from  their  estuaries.  In  the  Straits 
of  Pauxis,  in  the  river  of  the  Amazons,  more  than  five 
hundred  miles  from  the  sea,  the  tides  are  evident.  It 
requires  so  many  days  for  the  tide  to  ascend  this  mighty 
stream,  that  the  returning  tides  meet  a  succession  of 
those  which  are  coming  up ;  so  that  every  possible  vari- 
ety occurs  at  some  part  or  other  of  its  shores,  both  as 
to  magnitude  and  time.  It  requires  a  very  wide  expanse 
of  water  to  accumulate  the  impulse  of  the  sun  and  moon, 
so  as  to  render  their  influence  sensible ;  on  that  account 
the  tides  in  the  Mediterranean  and  Black  Sea  are 
scarcely  perceptible. 

These  perpetual  commotions  in  the  waters  are  occa- 
sioned by  forces  that  bear  a  very  small  proportion  to 
terrestrial  gravitation  :  the  sun's  action  in  raising  the 
ocean  is  only  the  ^^r¥VrroT  °f  gravitation  at  the  earth's 
surface,  and  the  action  of  the  moon  is  little  more  than 
twice  as  much ;  these  forces  being  in  the  ratio  of  1  to 
2-35333,  when  the  sun  and  moon  are  at  their  mean  dis- 
tances from  the  earth.  From  this  ratio  the  mass  of  the 
moon  is  found  to  be  only  the  ^  part  of  that  of  the  earth. 
Had  the  action  of  the  sun  on  the  ocean  been  exactly 
equal  to  that  of  the  moon,  there  would  have  been  no 
neap  tides,  and  the  spring  tides  would  have  been  of 
twice  the  height  which  the  action  of  either  the  sun  or 
moon  would  have  produced  separately ;  a  phenomenon 
depending  upon  the  interference  of  the  waves  or  undu- 
lations. 

A  stone  plunged  into  a  pool  of  still  water  occasions  a 
series  of  waves  to  advance  along  the  surface,  though  the 
water  itself  is  not  carried  forward,  but  only  rises  into 
heights  and  sinks  into  hollows,  each  portion  of  the  sur- 
face being  elevated  and  depressed  in  its  turn.  Another 
stone  of  the  same  size  thrown  into  the  water  near  the 
first,  will  occasion  a  similar  set  of  undulations.  Then  if 
an  equal  and  similar  wave  from  each  stone  arrive  at  the 
same  spot  at  the  same  time,  so  that  the  elevation  of  the 
one  exactly  coincides  with  the  elevation  of  the  other, 
their  united  effect  will  produce  a  wave  twice  the  size  of 


XIIL  INTERFERENCE  OF  WAVES.  .    93 

either.  But  if  one  wave  precede  the  other  by  exactly 
half  an  undulation,  the  elevation  of  the  one  will  coincide 
with  the  hollow  of  the  other,  and  the  hollow  of  the  one 
with  the  elevation  of  the  other ;  and  the  waves  will  so 
entirely  obliterate  one  another,  that  the  surface  of  the 
water  will  remain  smooth  and  level.  Hence  if  the  length 
of  each  wave  be  represented  by  1,  they  will  destroy  one 
another  at  intervals  of  ±,  £,  4,  &c.,  and  will  combine 
their  effects  at  the  intervals  1,  2,  3,  &c.  It  will  be  found 
according  to  this  principle,  when  still  water  is  disturbed 
by  the  fall  of  two  equal  stones,  that  there  are  certain 
lines  on  its  surface  of  a  hyperbolic  form,  where  the 
water  is  smooth  in  consequence  of  the  waves  oblitera- 
ting each  other ;  and  that  the  elevation  of  the  water  in 
the  adjacent  parts  corresponds  to  both  the  waves  united 
(N.  156).  Now  in  the  spring  and  neap  tides  arising 
from  the  combination  of  the  simple  soli-lunar  waves,  the 
spring  tide  is  the  joint  result  of  the  combination  when 
they  coincide  in  time  and  place ;  and  the  neap  tide  hap- 
pens when  they  succeed  each  other  by  half  an  interval, 
so  as  to  leave  only  the  effect  of  their  difference  sensible. 
It  is  therefore  evident  that  if  the  solar  and  lunar  tides 
were  of  the  same  height,  there  would  be  no  difference, 
consequently  no  neap  tides,  and  the  spring  tides  would 
be  twice  as  high  as  either  separately.  In  the  port  of 
Batsha  in  Tonquin,  where  the  tides  arrive  by  two  chan- 
nels of  lengths  corresponding  to  half  an  interval,  there 
is  neither  high  nor  low  water,  on  account  of  the  inter- 
ference of  the  waves. 

The  initial  state  of  the  ocean  has  no  influence  on  the 
tides;  for  whatever  its  primitive  conditions  may  have 
been,  they  must  soon  have  vanished  by  the  friction  and 
mobility  of  the  fluid.  One  of  the  most  remarkable  cir- 
cumstances in  the  theory  of  the  tides  is  the  assurance, 
that  in  consequence  of  the  density  of  the  sea  being  only 
one-fifth  of  the  mean  density  of  the  earth,  and  the  earth 
itself  increasing  in  density  toward  the  center,  the  sta- 
bility of  the  equilibrium  of  the  ocean  never  can  be  sub- 
verted by  any  physical  cause.  A  general  inundation 
arising  from  the  mere  instability  of  the  ocean  is  there- 
fore impossible.  A  variety  of  circumstances  however 
tend  to  produce  partial  variations  in  the  equilibrium  of 


94  CURRENTS  IN  THE  OCEAN.  SECT.  XIII. 

the  seas,  which  is  restored  by  means  of  currents.  Winds 
and  the  periodical  melting  of  the  ice  at  the  poles  occa- 
sion temporary  water-courses ;  but  by  far  the  most  im- 
portant causes  are  the  centrifugal  force  induced  by  the 
velocity  of  the  earth's  rotation,  and  variations  in  the 
density  of  the  sea. 

The  centrifugal  force  may  be  resolved  into  two  forces 
— one  perpendicular,  and  another  tangent  to  the  earth's 
surface  (N.  157).  The  tangential  force,  though  small, 
is  sufficient  to  make  the  fluid  particles  within  the  polar 
circles  tend  toward  the  equator,  and  the  tendency  is 
much  increased  by  the  immense  evaporation  in  the 
equatorial  regions  from  the  heat  of  the  sun,  which  dis- 
turbs the  equilibrium  of  the  ocean.  To  this  may  also 
be  added  the  superior  density  of  the  waters  near  the 
poles,  partly  from  their  low  temperature  and  partly 
from  their  gravitation  being  less  diminished  by  the  ac- 
tion of  the  sun  and  moon  than  that  of  the  seas  of  lower 
latitudes.  In  consequence  of  the  combination  of  all 
these  circumstances,  two  great  currents  perpetually  set 
from  each  pole  toward  the  equator.  But  as  they  come 
from  latitudes  where  the  rotatory  motion  of  the  surface 
of  the  earth  is  very  much  less  than  it  is  between  the 
tropics,  on  account  of  their  inertia,  they  do  not  im- 
mediately acquire  the  velocity  with  which  the  solid  part 
of  the  earth's  surface  is  revolving  at  the  equatorial  re- 
gions ;  from  whence  it  follows  that  within  twenty-five 
or  thirty  degrees  on  each  side  of  the  line,  the  ocean 
appears  to  have  a  general  motion  from  east  to  west, 
which  is  much  increased  by  the  action  of  the  trade 
winds.  This  mighty  mass  of  rushing  waters  at  about 
the  tenth  degree  of  south  latitude  is  turned  toward  the 
north-west  by  the  coast  of  America,  runs  through  the 
Gulf  of  Mexico,  and  passing  the  Straits  of  Florida  at 
the  rate  of  five  miles  an  hour,  forms  the  well-known 
current  of  the  Gulf-stream,  which  sweeps  along  the 
whole  coast  of  America  and  runs  northward  as  far  as 
the  bank  of  Newfoundland,  then  bending  to  the  east  it 
flows  past  the  Azores  and  Canary  islands,  till  it  joins 
the  great  westerly  current  of  the  tropics  about  latitude 
21°  north.  According  to  M.  de  Humboldt  this  great 
circuit  of  3800  leagues,  which  the  waters  of  the  Atlantic 


SECT.  XIII.  CURRENTS  IN  THE  OCEAN.  95 

are  perpetually  describing  between  the  parallels  of  eleven 
and  forty- three  degrees  of  latitude,  may  be  accomplished 
by  any  one  particle  in  two  years  and  ten  months.  In 
the  center  of  this  ^current  is  situated  the  wide  field  of 
floating  sea-weed  called  the  grassy  sea.  Besides  this 
there  are  branches  of  the  Gulf-stream,  which  convey 
the  fruits,  seeds,  and  a  portion  of  the  warmth  of  the 
tropical  climates  to  our  northern  shores. 

The  general  westward  motion  of  the  South  Sea,  togeth- 
er with  the  south  polar  current,  produce  various  water- 
courses in  the  Pacific  and  Indian  Oceans,  according  as 
the  one  or  the  other  prevails.  The  western  set  of  the 
Pacific  causes  currents  to  pass  on  each  side  of  Australia, 
while  the  polar  stream  rushes  along  the  bay  of  Bengal : 
the  westerly  current  again  becomes  most  powerful  to- 
ward Ceylon  and  the  Maldives,  whence  it  stretches  by 
the  extremity  of  the  Indian  peninsula  past  Madagascar, 
to  the  most  southern  point  of  the  continent  of  Africa, 
where  it  mingles  with  the  general  motion  of  the  seas. 
Icebergs  are  sometimes  drifted  as  far  as  the  Azores 
from  the  north  pole,  and  from  the  south  pole  they  have 
come  even  to  the  Cape  of  Good  Hope.  But  the  ice 
which  encircles  the  south  pole  extends  to  lower  latitudes 
by  10°  than  that  which  surrounds  the  north.  In  conse- 
quence of  the  polar  current  Sir  Edward  Parry  was 
obliged  to  give  up  his  attempt  to  reach  the  north  pole 
in  the  year  1827,  because  the  fields  of  ice  were  drifting 
to  the  south  faster  than  his  party  could  travel  over  them 
to  the  north. 

As  distinct  currents  of  air  traverse  the  atmosphere  in 
horizontal  strata,  so  in  all  probability  under  currents  in 
the  ocean  flow  in  opposite  directions  from  those  on  the 
surface  ;  and  there  is  every  reason  to  believe  that  the 
cold  waters,  deep  below  the  surface  of  the  sea  in  the 
equinoctial  regions,  are  brought  by  submarine  currents 
from  the  poles,  though  it  is  not  easy  to  prove  their  ex- 
istence. 


96  MOLECULAR  FORCES.  SBCT.  XIV. 


SECTION  XIV. 

Repulsive  Force  —  Interstices  or  Pores — Elasticity — Mossotti's  Theory — 
Gravitation  brought  under  the  same  law  with  Molecular  Attraction  and 
Repulsion — Gases  reduced  to  Liquids  by  Pressure — Intensity  of  the  Co- 
hesive Force — Effects  of  Gravitation — Effects  of  Cohesion — Minuteness 
of  the  ultimate  Atoms  of  Matter — Limited  Height  of  the  Atmosphere — 
Theory  of  Definite  Proportions  and  Relative  Weight  of  Atoms — Dr.  Far- 
aday's Discoveries  with  regard  to  Affinity — Composition  of  Water  by  a 
Plate  of  Platina — Crystallization — Cleavage — Isomorphism — Matter  con- 
sists of  Atoms  of  Definite  Form — Capillary  Attraction. 

THE  oscillations  of  the  atmosphere  and  its  action 
upon  rays  of  light  coming  from  the  heavenly  bodies, 
connect  the  science  of  astronomy  with  the  equilibrium 
and  movements  of  fluids,  and  the  laws  of  molecular 
attraction.  Hitherto  that  force  has  been  under  consid- 
eration which  acts  upon  masses  of  matter  at  sensible 
distances ;  but  now  the  effects  of  such  forces  are  to  be 
considered  as  act  at  inappreciable  distances  upon  the 
ultimate  atoms  of  material  bodies. 

All  substances  consist  of  an  assemblage  of  material 
particles,  which  are  far  too  small  to  be  visible  by  any 
means  human  ingenuity  has  yet  been  able  to  devise, 
and  which  are  much  beyond  the  limits  of  our  percep- 
tions. Since  every  known  substance  may  be  reduced 
in  bulk  by  pressure,  it  follows  that  the  particles  of  mat- 
ter are  not  in  actual  contact,  but  are  separated  by  inter- 
stices, owing  to  the  repulsive  principle  that  maintains 
them  at  extremely  minute  distances  from  one  another. 
It  is  evident  that  the  smaller  the  interstitial  spaces 
the  greater  the  density.  These  spaces  appear  in 
some  cases  to  be  filled  with  air,  as  may  be  infer- 
red from  certain  semi-opaque  minerals  and  other  sub- 
stances becoming  transparent  when  plunged  into  water ; 
sometimes  they  may  possibly  contain  some  unknown 
and  highly  elastic  fluid,  such  as  Sir  David  Brews ter  has 
discovered  in  the  minute  cavities  of  various  minerals, 
which  occasionally  causes  these  substances  to  explode 
with  violence  when  under  the  hands  of  the  lapidary, 
but  in  general  they  seem  to  our  senses  to  be  void ;  yet 
as  it  is  inconceivable  that  the  particles  of  matter  should 
vet  upon  one  another  without  some  means  of  commu- 


SECT.  XIV.  MOLECULAR  FORCES.  97 

nication,  tnere  is  eveiy  reason  to  presume  that  the  in- 
terstices of  material  substances  contain  a  portion  of  that 
subtle  ethereal  and  elastic  fluid  with  which  the  regions 
of  space  are  replete. 

Substances  compressed  by  a  sufficient  force,  are  said 
to  be  more  or  less  elastic  according  to  the  facility  with 
which  they  regain  their  bulk  or  volume  when  the 
pressure  is  removed ;  a  property  which  depends  upon 
the  repulsive  force  of  their  particles,  and  the  effort  re- 
quired to  compress  the  substance  is  a  measure  of  the 
intensity  of  that  repulsive  force  which  varies  with  the 
nature  of  the  substance. 

By  the  laws  of  gravitation  the  particles  of  matter 
attract  one  another  when  separated  by  sensible  dis- 
tances; and  as  they  repel  each  other  when  they  are 
inappreciably  near,  it  recently  occurred  to  Professor 
Mossotti  of  Pisa,  that  there  might  be  some  intermedi- 
ate distance  at  which  the  particles  might  neither  attract 
nor  repel  one  another,  but  remain  balanced  in  that 
stable  equilibrium  which  they  are  found  to  maintain  in 
every  material  substance  solid  and  fluid. 

It  has  long  been  a  hypothesis  among  philosophers 
that  electricity  is  the  agent  which  binds  the  particles  of 
matter  together.  We  are  totally  ignorant  of  the  nature 
of  electricity,  but  it  is  generally  supposed  to  be  an  ethe- 
real fluid  in  the  highest  state  of  elasticity  surrounding 
every  particle  of  matter ;  and  as  the  earth  and  the  at- 
mosphere are  replete  with  it  in  a  latent  state,  there  is 
every  reason  to  believe  that  it  is  unbounded,  filling  the 
regions  of  space. 

The  celebrated  Franklin  was  the  first  who  explained 
the  phenomena  of  electricity  in  repose,  by  supposing 
the  molecules  of  bodies  to  be  surrounded  by  an  atmos- 
phere of  the  electric  fluid  ;  and  that  while  the  electric 
atoms  repel  one  another,  they  are  attracted  by  the  ma- 
terial molecules  of  the  body.  These  forces  of  attraction 
and  repulsion  were  afterward  proved  by  Coulomb  to 
vary  inversely  as  the  squares  of  the  distance.  The 
hypothesis  of  Franklin  waa  reduced  to  a  mathematical 
theory  by  JEpinus,  and  the  most  refined  analysis  has 
been  employed  by  the  Baron  Poisson  in  explanation  of 
electric  phenomena.  Still  these  philosophers  were  un- 


98  MOSSOnTS  THEORY.  SECT.  XIV. 

able  to  reconcile  the  attraction  of  the  molecules  of  mat- 
ter inversely  as  the  squares  of  the  distance  as  proved 
by  Newton,  with  their  mutual  repulsion  according  to 
the  same  law.  But  Professor  Mossotti  has  recently 
shown,  by  a  very  able  analysis,  that  there  are  strong 
grounds  for  believing  that  not  only  the  molecular  forces 
which  unite  the  particles  of  material  bodies  depend  on 
the  electric  fluid,  but  that  even  gravitation  itself,  which 
binds  world  to  world  and  sun  to  sun,  can  no  longer  be 
regarded  as  an  ultimate  principle,  but  the  residual  por- 
tion of  a  far  more  powerful  force  generated  by  that  en- 
ergetic agent  which  pervades  creation. 

It  is  true  that  this  connection  between  the  molecular 
forces  and  gravitation  depends  upon  a  hypothesis ;  but 
in  the  greater  number  of  physical  investigations,  some 
hypothesis  is  requisite  in  the  first  instance  to  aid  the 
imperfection  of  our  senses.  Yet,  when  the  phenomena 
of  nature  accord  with  the  assumption,  we  are  justified 
in  believing  it  to  be  a  general  law. 

As  the  particles  of  material  bodies  are  not  in  actual 
contact,  Professor  Mossotti  supposes  that  each  is  en- 
compassed by  an  atmosphere  of  the  ethereal  fluid; 
that  the  atoms  of  the  fluid  repel  one  another ;  that  the 
molecules  of  matter  repel  one  another,  but  with  less 
intensity ;  and  that  there  is  a  mutual  attraction  be- 
tween the  particles  of  matter  and  the  atoms  of  the  fluid. 
Forces  which  we  know  to  exist,  and  which  he  assumes 
to  vary  inversely  as  squares  of:  the  distance.  The  fol- 
lowing important  results  have  been  obtained  by  the  pro- 
fessor from  the  adjustment  of  these  three  forces  : — 

When  the  material  molecules  of  a  body  are  inappre- 
ciably near  to  one  another,  they  mutually  repel  each 
other  with  a  force  which  diminishes  rapidly  as  the 
infinitely  small  distance  between  the  material  molecules 
augments,  and  at  last  vanishes.  When  the  molecules 
are  still  farther  apart,  the  force  becomes  attractive.  At 
that  particular  point  where  the  change  takes  place,  the 
forces  of  repulsion  and  attraction  balance  each  other,  so 
that  the  molecules  of  a  body  are  neither  disposed  to 
approach  nor  recede,  but  remain  in  equilibrio.  If  we 
try  to  press  them  nearer,  the  repulsive  force  resists  the 
attempt ;  and  if  we  endeavor  to  break  the  body  so  as  to 


S«CT  XIV.  MOSSOTTPS  THEORY.  99 

tear  the  particles  asunder,  the  attractive  force  predom- 
inates and  keeps  them  together.  This  is  what  consti- 
tutes the  cohesive  force,  or  force  of  aggregation,  by 
which  the  molecules  of  all  substances  are  united.  The 
limits  of  the  distance  at  which  the  negative  action  be- 
comes positive  vary  according  to  the  temperature  and 
nature  of  the  molecules,  and  determine  whether  the 
body  which  they  form  be  solid,  liquid,  or  aeriform. 

Beyond  this  neutral  point,  the  attractive  force  in 
creases  as  the  distance  between  the  molecules  augments, 
till  it  attains  a  ,maximum ;  when  the  particles  are  more 
apart  it  diminishes ;  and  as  soon  as  they  are  separated 
by  finite  or  sensible  distances,  it  varies  directly  as  their 
mass  and  inversely  as  the  squares  of  the  distance, 
which  is  precisely  the  law  of  universal  gravitation. 

Thus  on  the  hypothesis  that  the  mutual  repulsion 
between  the  electric  atoms  is  a  little  more  powerful 
than  the  mutual  repulsion  between  the  particles  of  mat- 
ter, the  ether  and:  the  matter  attract  each  other  with 
unequal  intensities,  which  leave  an  excess  .of  attractive 
force  constituting  gravitation.  As  the  gravitating  force 
is  in  operation  wherever  there  is  matter,  the  ethereal 
electric  fluid  must  encompass  all  the  bodies  in  the  uni- 
verse ;  and  as  it  is  utterly  incomprehensible  that  the 
celestial  bodies  should  exert  a  reciprocal  attraction 
through  a  void,  this  important  investigation  of  Professor 
Mossotti  furnishes  additional  presumption  in  favor  of  a 
universal  ether,  already  all  but  proved  by  the  motion  of 
comets  and  the  theory  of  light. 

In  ae'riform  fluids  the  particles  of  matter  are  more 
remote  from  each  other  than  in  liquids  and  solids ;  but 
the  pressure  may  be  so  great  as  to  reduce  an  ae'riform 
fluid  to  a  liquid,  and  a  liquid  to  a  solid.  Dr.  Faraday 
has  reduced  some  of  the  gases  to  a  liquid  state  by  very 
great  compression;  but  although  atmospheric  air  is 
capable  of  a  diminution  of  volume  to  which  we  do  not 
know  the  limit,  it  has  hitherto  always  retained  its 
gaseous  properties,  and  resumes  its  primitive  volume 
the  instant  the  pressure  is  removed. 

If  the  particles  approach  sufficiently  near  to  produce 
equilibrium  between  the  attractive  and  repulsive  forces, 
but  not  near  enough  to  admit  of  any  influence  from 


100  CONSTITUTION  OF  BODIES.  S¥CT.  XIV. 

their  form,  perfect  mobility  will  exist  among  them  re- 
sulting from  the  similarity  of  their  attractions,  and  they 
will  offer  great  resistance  when  compressed  ;  properties 
which  characterize  liquids  in  which  the  repulsive  prin- 
ciple is  greater  than  in  the  gases.  When  the  distance 
between  the  particles  is  still  less,  solids  are  formed. 
But  the  nature  of  their  structure  will  vary,  because  at 
such  small  distances  the  power  of  the  mutual  attraction 
of  the  particles  will  depend  upon  their  form,  and  will 
be  modified  by  the  sides  they  present  to  one  another 
during  their  aggregation.  Besides  these  three  condi- 
tions of  matter,  there  are  an  infinite  variety  of  others 
corresponding  to  the  various  limits  at  which  the  two 
contending  forces  are  balanced,  which  may  be  observed 
in  the  fusion  of  metals,  and  other  substances  passing 
from  hardness  to  toughness,  viscidity,  and  through  all 
the  other  stages  to  perfect  fluidity  and  even  to  vapor. 

The  effort  required  to  break  a  substance  is  a  measure 
of  the  intensity  of  the  cohesive  force  exerted  by  its 
particles,  which  is  as  variable  as  the  intensity  of  the 
repulsive  principle.  In  stone,  iron,  steel,  and  all  brittle 
and  hard  bodies,  the  cohesion  of  the  particles  is  powerful 
but  of  small  extent.  In  elastic  substances,  on  the  con- 
trary, its  action  is  weak  but  more  extensive.  Since  all 
bodies  expand  by  heat,  the  cohesive  force  is  weakened 
by  an  increase  of  temperature. 

Every  particle  of  matter,  whether  it  forms  a  con- 
stituent part  of  a  solid,  liquid,  or  aeriform  fluid,  is 
subject  to  the  law  of  gravitation.  The  weight  of  the 
atmosphere,  of  gases  and  vapor,  shows  that  they  consist 
of  gravitating  particles.  In  liquids  the  cohesive  force 
is  not  sufficiently  powerful  to  resist  the  action  of  gravi- 
tation. Therefore  although  their  component  particles 
-still  maintain  their  connection,  the  liquid  is  scattered  by 
their  weight,  unless  when  it  is  confined  in  a  vessel  or 
has  already  descended  to  the  lowest  point  possible,  and 
assumed  a  level  surface  from  the  mobility  of  its  particles 
and  the  influence  of  the  gravitating  force,  as  in  the 
ocean,  or  a  lake.  Solids  would  also  fall  to  pieces  by 
the  weight  of  their  particles,  if  the  force  of  cohesion 
were  not  powerful  enough  to  resist  the  efforts  of  gravi- 
tation. 


SECT.  XIV.  COHESION.  101 

The  phenomena  arising  from  the  force  of  cohesion 
are  innumerable.  The  spherical  form  of  rain  drops ; 
the  difficulty  of  detaching  a  plate  of  glass  from  the  sur- 
face of  water ;  the  force  with  which  two  plane  surfaces 
adhere  when  pressed  together;  the  drops  that  cling  to 
the  window-glass  in'a  shower  of  rain — are  all  effects  of 
cohesion  entirely  independent  of  atmospheric  pressure, 
and  are  included  in  the  same  analytical  formula  (N. 
158)  which  expresses  all  the  circumstances  accurately, 
although  the  laws  according  to  which  the  forces  of 
cohesion  and  repulsion  vary  are  unknown.  It  is  more 
than  probable  that  the  spherical  form  of  the  sun  and 
planets  is  due  to  the  force  of  cohesion,  as  they  have 
every  appearance  of  having  been  at  one  period  in  a  state 
of  fusion. 

A  very  remarkable  instance  of  cohesion  has  occasion- 
ally been  observed  hi  piate-glass  manufactories.  After 
the  large  plates  of  glass  of  which  the  mirrors  are  to  be 
made  have  received  their  last  polish,  they  are  carefully 
wiped  and  laid  on  their  edges  with  their  surfaces  resting 
on  one  another.  In  the  course  of  time  the  cohesion 
has  sometimes  been  so  powerful,  that  they  could  not  be 
separated  without  breaking.  -  Instances  have  occurred 
where  two  or  three  have  been  so  perfectly  united,  that 
they  have  been  cut  and  their  edges  polished  as  if  they 
had  been  fused  together,  and  so  great  was  the  force 
required  to  make  their  surfaces  slide  that  one  tore  off  a 
portion  of  the  surface  of  the  other. 

The  size  of  the  ultimate  particles  of  matter  must  be 
small  in  the  extreme.  Organized  beings  possessing  life 
and  all  its  functions,  have  been  discovered  so  small  that 
a  million  of  them  would  occupy  less  space  than  a  grain 
of  sand.  The  malleability  of  gold,  the  perfume  of 
musk,  the  odor  of  flowers,  and  many  other  instances 
might  be  given  of  the  excessive  minuteness  of  the 
atoms  of  matter ;  yet  from  a  variety  of  circumstances  it 
may  be  inferred  that  matter  is  not  infinitely  divisible. 
Dr.  Wollaston  has  shown  that  in  all  probability  the 
atmospheres  of  the  sun  and  planets  as  well  as  of  the 
earth  consist  of  ultimate  atoms  no  longer  divisible  ;  and 
if  so,  that  our  atmosphere  only  extends  to  that  point 
where  the  terrestrial  attraction  is  balanced  by  the  elas- 


102  DEFINITE  PROPORTIONS.  SECT.  XIV. 

ticity  of  the  air.  The  definite  proportions  of  chemical 
compounds  afford  one  of  the  best  proofs  that  divisibility 
of  matter  has  a  limit.  The  cohesive  force  which  has 
been  the  subject  of  the  preceding  considerations,  only 
unites  particles  of  the  same  kind  of  matter ;  whereas 
affinity,  which  is  the  cause  of  chemical  compounds,  is 
the  mutual  attraction  between  particles  of  different 
kinds  of  matter,  and  is  merely  a  result  of  the  electrical 
state  of  the  particles,  chemical  affinity  and  electricity 
being  only  forms  of  the  same  powers. 

It  is  a  permanent  and  universal  law  in  all  unorganized 
bodies  hitherto  analyzed,  that  the  composition  of  sub- 
stances is  definite  and  invariable,  the  same  compound 
always  consisting  of  the  same  elements  united  together 
in  the  same  proportions.  Two  substances  may  indeed 
be  mixed ;  but  they  will  not  combine  to  form  a  third 
substance  different  from  both,  unless  their  component 
particles  unite  in  definite  proportions,  that  is  to  say,  one 
part  by  weight  of  one  of  the  substances  will  unite  with 
one  part  by  weight  of  the  other,  or  with  two  parts,  or 
three,  or  four,  &c.,  so  as  to  form  a  new  substance ;  but 
in  any  other  proportions  they  will  only  be  mechanically 
mixed.  For  example,  one  part  by  weight  of  hydrogen 
gas  will  combine  with  eight  parts  by  weight  of  oxygen 
gas  and  form  water ;  or  it  will  unite  with  sixteen  parts 
by  weight  of  oxygen,  and  form  a  substance  called 
deutoxide  of  hydrogen ;  but  added  to  any  other  weight 
of  oxygen,  it  will  produce  one  or  both  of  these  com- 
pounds mingled  with  the  portion  of  oxygen  or  hydrogen 
in  excess.  The  law  of  definite  proportion  established 
by  Dr.  Dalton,  on  the  principle  that  eveiy  compound 
body  consists  of  a  combination  of  the  atoms  of  its  con- 
stituent parts,  is  of  universal  application,  and  is  in  fact 
one  of  the  most  important  discoveries  in  physical  science, 
furnishing  information  previously  unhoped  for  with  re- 
gard to  the  most  secret  and  minute  operations  of  nature, 
in  disclosing  the  relative  weights  of  the  ultimate  atoms 
of  matter.  Thus  an  atom  of  oxygen  uniting  with  an 
atom  of  hydrogen  forms  the  compound  water ;  but  as 
every  drop  of  water,  however  small,  consists  of  eight 
parts  by  weight  of  oxygen  and  one  part  by  weight  of 
hydrogen,  it  follows  that  an  atom  of  oxygen  is  eight 


S«cr.  XIV.  CHEMICAL  AFFINITY.  103 

times  heavier  than  an  atom  of  hydrogen.  In  the  same 
manner  sulphuretted  hydrogen  gas  consists  of  sixteen 
parts  by  weight  of  sulphur  and  one  of  hydrogen ;  there- 
fore, an  atom  of  sulphur  is  sixteen  times  heavier  than 
an  atom  of  hydrogen.  Also  carbonic  oxide  is  consti- 
tuted of  six  parts  by  weight  of  carbon,  and  eight  of 
oxygen ;  and  as  an  atom  of  oxygen  has  eight  times  the 
weight  of  an  atom  of  hydrogen,  it  follows  that  an  atom 
of  carbon  is  six  times  heavier  than  one  of  hydrogen. 
Since  the  same  definite  proportion  holds  in  the  compo- 
sition of  all  substances  that  have  been  examined,  it  may 
be  concluded  that  there  are  great  differences  in  the 
weights  of  the  ultimate  particles  of  matter.  M.  Gay 
Lussac  discovered  that  gases  unite  together  by  their 
bulk  or  volumes,  in  such  simple  and  definite  proportions 
as  one  to  one,  one  to  two,  one  to  three,  &c.  For 
example,  one  volume  or  measure  of  oxygen  unites  wkh 
two  volumes  or  measures  of  hydrogen  in  the  formation 
of  water. 

Affinity  modified  by  the  electrical  condition  of  the 
particles  of  matter,  has  hitherto  been  believed  to  be  the 
cause  of  chemical  combinations.  However,  Dr.  Fara- 
day has  proved  by  experiments,  on  bodies  both  in  solu- 
tion and  fusion,  that  chemical  affinity  is  merely  a  result 
of  the  electrical  state  of  the  particles  of  matter.  Now 
it  must  be  observed  that  the  composition  of  bodies  as 
well  as  their  decomposition,  may  be  accomplished  by 
means  of  electricity ;  and  Dr.  Faraday  has  found  that 
this  chemical  composition  and  decomposition,  by  a. given 
current  of  electricity,  is  always  accomplished  according 
to  the  laws  of  definite  proportions ;  and  that  the  quan- 
tity of  electricity  requisite  for  the  decomposition  of  a 
substance  is  exactly  the  quantity  necessary  for  its  com- 
position. Thus  the  quantity  of  electricity  which  can. 
decompose  a  grain  weight  of  water  is  exactly  equal  to 
the  quantity  of  electricity  which  unites  the  elements  of 
that  grain  of  water  together,  and  is  equivalent  to  the 
quantity  of  atmospheric  electricity  which  is  active  in  a 
very  powerful  thunder-storm.  These  laws  are  univer- 
sal, and  are  of  that  high  and  general  order  that  charac- 
terize all  great  discoveries,  and  perfectly  agree  with 
Professor  Mossotti's  theory. 


104  EFFECTS  OF  COHESION.  SECT.  XIV. 

Dr.  Faraday  has  given  a  singular  instance  of  cohesive 
force  inducing  chemical  combination,  by  the  following 
experiment,  which  seems  to  be  nearly  allied  to  the  dis- 
covery made  by  M.  Dcebereiner,  in  1823,  of  the  spon- 
taneous combustion  of  spongy  platina  (N.  159)  exposed 
to  a  stream  of  hydrogen  gas  mixed  with  common  air. 
A  plate  of  platina  with  extremely  clean  surfaces,  when 
plunged  into  oxygen  and  hydrogen  gas  mixed  in  the  pro- 
portions which  are  found  in  the  constitution  of  water, 
causes  the  gases  to  combine  and  water  to  be  formed, 
the  platina  to  become  red-hot,  and  at  last  an  explosion 
to  take  place ;  the  only  conditions  necessary  for  this 
curious  experiment  being  excessive  purity  in  the  gases 
and  in  the  surface  of  the  plate.  A  sufficiently  pure 
metallic  surface  can  only  be  obtained  by  immersing  the 
platina  in  very  strong  hot  sulphuric  acid  and  then  wash- 
ing it  in  distilled  water,  or  by  making  it  the  positive 
pole  of  a  pile  in  dilute  sulphuric  acid.  It  appears  that 
the  force  of  cohesion  as  well  as  the  force  of  affinity  ex- 
erted by  particles  of  matter,  extends  to  all  the  particles 
within  a  very  minute  distance.  Hence  the  platina  while 
drawing  the  particles  of  the  two  gases  toward  its  sur- 
face by  its  great  cohesive  attraction,  brings  them  so  near 
to  one  another  that  they  come  within  the  sphere  of  their 
mutual  affinity,  and  a  chemical  combination  takes  place. 
Dr.  Faraday  attributes  the  effect  in  part  also  to  a  dim- 
inution in  the  elasticity  of  the  gaseous  particles  on  their 
sides  adjacent  to  the  platina,  and  to  their  perfect  mix- 
ture or  association,  as  well  as  to  the  positive  action  of 
the  metal  in  condensing  them  against  its  surface  by  its 
attractive  force.  The  particles  when  chemically  united 
run  off  the  surface  of  the  metal  in  the  form  of  water  by 
their  gravitation,  or  pass  away  as  aqueous  vapor  and  make 
way  for  others. 

The  particles  of  matter  are  so  small  that  nothing  is 
known  of  their  form,  further  than  the  dissimilarity  of 
their  different  sides  in  certain  cases,  which  appears  from 
then*  reciprocal  attractions  during  crystalization  being 
more  or  less  powerful,  according  to  the  sides  they  pre- 
sent to  one  another.  Crystalization  is  an  effect  of  mole- 
cular attraction  regulated  by  certain  laws,  according  to 
which  atoms  of  the  same  kind  of  matter  unite  in  regu- 


SECT.  XIV.  CRYSTALIZATION.  105 

lar  forms — a  fact  easily  proved  by  dissolving  a  piece  of 
alum  in  pure  water.  The  mutual  attraction  of  the  par- 
ticles is  destroyed  by  the  water ;  but  if  it  be  evaporated 
they  unite  and  form  in  uniting  eight-sided  figures  called 
octahedrons  (N.  160).  These,  however,  are  not  all  the 
same.  Some  have  their  angles  cut  off,  others  their 
edges,  and  some  both,  while  the  remainder  take  the 
regular  form.  It  is  quite  clear  that  the  same  circum- 
stances which  cause  the  aggregation  of  a  few  particles 
would,  if  continued,  cause  the  addition  of  more ;  and 
the  process  would  go  on  as  long  as  any  particles  remain 
free  round  the  primitive  nucleus,  which  would  increase 
in  size,  but  would  remain  unchanged  in  form,  the  figure 
of  the  particles  being  such  as  to  maintain  the  regularity 
and  smoothness  of  the  surfaces  of  the  solid  and  their 
mutual  inclinations.  A  broken  crystal  will  by  degrees 
resume  its  regular  figure  when  put  back  again  into  the 
solution  of  alum,  which  shows  that  the  internal  and  ex- 
ternal particles  are  similar  and  have  a  similar  attraction 
for  the  particles  held  in  solution.  The  original  condi- 
tions of  aggregation  which  make  the  molecules  of  the 
same  substance  unite  in  different  forms  must  be  very 
numerous,  since  of  carbonate  of  lime  alone  there  are 
many  hundred  varieties ;  and  certain  it  is  from  the  mo- 
tion of  polarized  light  through  rock  crystal,  that  a  very 
different  arrangement  of  particles  is  requisite  to  produce 
an  extremely  small  change  in  external  form.  A  variety 
of  substances  in  crystalizing  combine  chemically  with  a 
certain  portion  of  water  which  in  a  dry  state  forms  an 
essential  part  of  their  crystals ;  and  according  to  the 
experiments  of  MM.  Haidinger  and  Mitscherlich  seems 
in  some  cases  to  give  the  peculiar  determination  to  their 
constituent  molecules.  These  gentlemen  have  observed 
that  the  same  substance  crystalizing  at  different  tem- 
peratures unites  with  different  quantities  of  water  and 
assumes  a  corresponding  variety  of  forms.  Seleniate 
of  zinc,  for  example,  unites  with  three  different  portions 
of  water  and  assumes  three  different  forms,  according 
as  its  temperature  in  the  act  of  crystalizing  is  hot,  luke- 
warm, or  cold.  Sulphate  of  soda,  also,  which  crystal- 
izes  at  90°  of  Fahrenheit  without  water  of  crystaliza- 
tion,  combines  with  water  at  the  ordinary  temperature 


106  CRYSTALIZATION.  SBCT.  XIV. 

and  takes  a  different  form.  Heat  appears  to  have  a 
great  influence  on  the  phenomena  of  crystalization,  not 
only  when  the  particles  of  matter  are  free,  but  even 
when  firmly  united,  for  it  dissolves  their  union  and  gives 
them  another  determination.  Professor  Mitscherlich 
found  that  prismatic  crystals  of  sulphate  of  nickel  (N.  161 ) 
exposed  to  a  summer's  sun  in  a  close  vessel,  had  their 
internal  structure  so  completely  altered  without  any  ex- 
terior change,  that  when  broken  open  they  were  com- 
posed internally  of  octahedrons  with  square  bases.  The 
original  aggregation  of  the  internal  particles  had  been 
dissolved,  and  a  disposition  given  to  arrange  themselves 
in  a  crystaline  form.  'Crystals  of  sulphate  of  magnesia 
and  of  sulphate  of  zinc,  gradually  heated  in  alcohol  till  it 
boils,  lose  their  transparency  by  degrees,  and  when 
opened  are  found  to  consist  of  innumerable  minute  crys- 
tals totally  different  in  form  from  the  whole  crystals ; 
and  prismatic  crystals  of  zinc  (N.  162)  are  changed  in  a 
few  seconds  into  octahedrons  by  the  heat  of  the  sun: 
other  instances  might  be  given  of  the  influence  of  even 
moderate  degrees  of  temperature  on  molecular  attrac- 
tion in  the  interior  of  substances.  It  must  be  observed 
that  these  experiments  give  entirely  new  views  with 
regard  to  the  constitution  of  solid  bodies.  We  are  led 
from  the  mobility  of  fluids  to  expect  great  changes  in 
the  relative  positions  of  their  molecules,  which  must  be 
in  perpetual  motion  even  in  the  stillest  water  or  calmest 
air ;  but  we  were  not  prepared  to  find  motion  to  such 
an  extent  in  the  interior  of  solids.  That  their  particles 
are  brought  nearer  by  cold  and  pressure,  or  removed 
farther  from  one  another  by  heat,  might  be  expected ; 
but  it  could  not  have  been  anticipated  that  their  relative 
positions  could  be  so  entirely  changed  as  to  alter  their 
mode  of  aggregation.  It  follows  from  the  low  temper- 
ature at  which  these  changes  are  effected,  that  there 
is  probably  no  portion  of  inorganic  matter  that  is  not  in 
a  state  of  relative  motion. 

Professor  Mitscherlich's  discoveries  with  regard  to 
the  forms  of  crystalized  substances,  as  connected  with 
their  chemical  charcter,  have  thrown  additional  light  on 
the  constitution  of  material  bodies.  There  is  a  certain 
set  of  crystaline  forms  which  are  not  susceptible  of 


8«CT.  XIV.  ISOMORPHISM.  107 

variation,  as  the  die  or  cube  (N.  163),  which  may  be 
small  or  large,  but  is  invariably  a  solid  bounded  by  six 
square  surfaces  or  planes.  Such  also  is  the  tetrahedron 
(N.  164)  or  four-sided  solid  contained  by  four  equal- 
sided  triangles.  Several  other  solids  belong  to  this  class, 
which  is  called  the  Tessular  system  of  crystalization. 
There  are  other  crystals  which,  though  bounded  by  the 
same  number  of  sides,  and  having  the  same  form,  are 
yet  susceptible  of  variation ;  for  instance,  the  eight- 
sided  figure  with  a  square  base  called  an  octahedron 
(N.  165),  which  is  sometimes  flat  and  low  and  some- 
times acute  and  high.  It  was  formerly  believed  that 
identity  of  form  in  all  crystals  not  belonging  to  the 
Tessular  system  indicated  identity  of  chemical  compo- 
sition. Professor  Mitscherlich  however  has  shown, 
that  substances  differing  to  a  certain  degree  in  chemical 
composition  have  the  property  of  assuming  the  same 
crystaline  form.  For  example,  the  neutral  phosphate 
of  soda  and  the  arseniate  of  soda  crystalize  in  the  very 
same  form,  contain  the  same  quantities  of  acid,  alkali, 
and  water  of  crystalization  ;  yet  they  differ  so  far,  that 
one  contains  arsenic  and  the  other  an  equivalent  quan- 
tity of  phosphorus.  Substances  having  such  properties 
are  said  to  be  isomorphous,  that  is,  equal  in  form.  Of 
these  there  are  many  groups,  each  group  having  the 
same  form,  and  similarity  though  not  identity  of  chemi- 
cal composition.  For  instance,  one  of  the  isomorphous 
groups  is  that  consisting  of  certain  chemical  substances 
called  the  protoxides  of  iron,  copper,  zinc,  nickel,  and 
manganese,  all  of  which  are  identical  in  form  and  contain 
the  same  quantity  of  oxygen,  but  differ  in  the  respective 
metals  they  contain,  which  are  however  nearly  in  the 
same  proportion  in  each.  All  these  circumstances  tend 
to  prove  that  substances  having  the  same  crystaline  form 
must  consist  of  ultimate  atoms,  having  the  same  figure 
and  arranged  in  the  very  same  order  ;  so  that  the  form 
of  crystals  is  dependent  on  their  atomic  constitution. 

All  crystalized  bodies  have  joints  called  cleavages,  at 
which  they  split  more  easily  than  in  other  directions ; 
on  this  property  the  whole  art  of  cutting  diamonds  de- 
pends. Each  substance  splits  in  a  manner  and  informs 
peculiar  to  itself.  For  example,  all  the  hundreds  of 


108  CLEAVAGE.  SECT.  XIV. 

forms  of  carbonate  of  lime  split  into  six-sided  figures, 
called  rhombohedrons  (N.  166),  whose  alternate  angles 
measure  105°*55  and  75°-05,  however  far  the  division 
may  be  carried ;  therefore  the  ultimate  particle  of  car- 
bonate of  lime  is  presumed  to  have  that  form.  However 
this  may  be,  it  is  certain  that  all  the  various  crystals  of 
that  mineral  may  be  formed  by  building  up  six-sided 
solids  of  the  form  described,  in  the  same  manner  as  chil- 
dren build  houses  with  miniature  bricks.  It  may  be 
imagined  that  a  wide  difference  may  exist  between  the 
particles  of  an  unformed  mass,,  and  a  crystal  of  the  same 
substance  —  between  the  common  shapeless  limestone 
and  the  pure  and  limpid  crystal  of  Iceland  spar,  yet 
chemical  analysis  detects  none  ;  their  ultimate  atoms 
are  identical,  and  crystalization  shows  that  the  difference 
arises  only  from  the  mode  of  aggregation.  Besides,  all 
substances  either  crystalize  naturally,  or  may  be  made  to 
do  so  by  art.  Liquids  crystalize  in  freezing,  vapors  by 
sublimation  (N.  167)  ;  and  hard  bodies,  when  fused,  crys- 
talize in  cooling.  Hence  it  may  be  inferred  that  all  sub- 
stances are  composed  of  atoms,  on  whose  magnitude, 
density,  and  form  their  nature  and  qualities  depend ; 
and  as  these  qualities  are  unchangeable,  the  ultimate 
particles  of  matter  must  be  incapable  of  wear — the  same 
now  as  when  created. 

The  oscillations  of  the  atmosphere  and  the  changes 
in  its  temperature,  are  measured  by  variations  in  the 
heights  of  the  barometer  and  thermometer.  But  the 
actual  length  pf  the  liquid  columns  depends  not  only  upon 
the  force  of  gravitation,  but  upon  the  cohesive  force,  or 
reciprocal  attraction  between  the  molecules  of  the  liquid 
and  those  of  the  tube  containing  it.  This  peculiar  action 
of  the  cohesive  force  is  called  capillary  attraction  or  ca- 
pillarity. If  a  glass  tube  of  extremely  fine  bore,  such  as 
a  small  thermometer  tube,  be  plunged  into  a  cup  of  wa- 
ter or  spirit  of  wine,  the  liquid  will  immediately  rise  in 
the  tube  above  the  level  of  that  in  the  cup  ;  and  the  sur- 
face of  the  little  column  thus  suspended  will  be  a  hollow 
hemisphere,  whose  diameter  is  the  interior  diameter  of 
the  tube.  If  the  same  tube  be  plunged  into  a  cupful  of 
mercury  the  liquid  will  also  rise  in  the  tube,  but  it  will 
never  attain  the  level  of  that  in  the  cup,  and  its  surfnce 


SECT.  XIV.  CAPILLARY  ATTRACTION.  109 

will  be  a  hemisphere  whose  diameter  is  also  the  diame- 
ter of  the  tube  (N.  168).  The  elevation  or  depression 
of  the  same  liquid  in  different  tubes  of  the  same  matter, 
is  in  the  inverse  ratio  of  their  internal  diameters  (N.  169), 
and  altogether  independent  of  their  thickness ;  whence 
it  follows  that  the  molecular  action  is  insensible  at  sen- 
sible distances,  and  that  it  is  only  the  thinnest  possi- 
ble film  of  the  interior  surface  of  the  tubes  that  exerts  a 
sensible  action  on  the  liquid.  So  much  indeed  is  this 
the  case,  that  when  tubes  of  the  same  bore  are  com- 
pletely wetted  with  water  throughout  their  whole  ex- 
tent, mercury  will  rise  to  the  same  height  in  all  of  them, 
whatever  be  their  thickness  or  density,  because  the  mi- 
nute coating  of  moisture  is  sufficient  to  remove  the  in- 
ternal column  of  mercury  beyond  the  sphere  of  attraction 
of  the  tube,  and  to  supply  the  place  of  a  tube  by  its 
own  capillary  attraction.  The  forces  which  produce  the 
capillary  phenomena  are  the  reciprocal  attraction  of  the 
tube  and  the  liquid,  and  of  the  liquid  particles  on  one 
another ;  and  in  order  that  the  capillary  column  may  be 
in  equilibrio,  the  weight  of  that  part  of  it  which  rises 
above  or  sinks  below  the  level  of  the  liquid  in  the  cup 
must  balance  these  forces. 

The  estimation  of  the  action  of  the  liquid  is  a  difficult 
part  of  this  problem.  La  Place,  Dr.  Young,  and  other 
mathematicians,  have  considered  the  liquid  within  the 
tube  to  be  of  uniform  density ;  but  M.  Poisson,  in  one 
of  those  masterly  productions  in  which  he  elucidates  the 
most  abstruse  subjects,  has  proved  that  the  phenomena 
of  capillary  attraction  depend  upon  a  rapid  decrease  in 
the  density  of  the  liquid  column  throughout  an  extremely 
small  space  at  its  surface.  Every  indefinitely  thin  layer 
of  a  liquid  is  compressed  by  the  liquid  above  it,  and  sup- 
ported by  that  below.  Its  degree  of  condensation  de- 
pends upon  the  magnitude  of  the  compression  force ; 
and  as  this  force  decreases  rapidly  toward  the  surface 
where  it  vanishes,  the  density  of  the  liquid  decreases 
also.  M.  Poisson  has  shown  that  when  this  force  is 
omitted,  the  capillary  surface  becomes  plane,  and  that 
the  liquid  in  the  tube  will  neither  rise  above  nor  sink 
below  the  level  of  that  in  the  cup.  In  estimating  the 
forces,  it  is  also  necessary  to  include  the  variation  in  the 
K. 


110  CAPILLARY  ATTRACTION.  SHCT.  XIV. 

density  of  the  capillary  surface  round  the  edges  from  the 
attraction  of  the  tube. 

The  direction  of  the  resulting  force  determines  the 
curvature  of  the  surface  of  the  capillary  column.  In 
order  that  a  liquid  may  be  in  equilibrio,  the  force  re- 
sulting from  all  the  forces  acting  upon  it  must  be  per- 
pendicular to  the  surface.  Now  it  appears  that  as  glass 
is  more  dense  than  water  or  alcohol,  the  resulting  force 
will  be  inclined  toward  the  interior  side  of  the  tube  ; 
therefore  the  surface  of  the  liquid  must  be  more  ele- 
vated at  the  sides  of  the  tube  than  in  the  center  in  order 
to  be  perpendicular  to  it,  so  that  it  will  be  concave  as  in 
the  thermometer.  But,  as  glass  is  less  dense  than  mer- 
cury, the  resulting  force  will  be  inclined  from  the  interior 
side  of  the  tube  (N.  170),  so  that  the  surface  of  the  ca- 
pillary column  must  be  more  depressed  at  the  sides  of 
the  tube  than  in  the  center,  in  order  to  be  perpendicular 
to  the  resulting  force,  and  is  consequently  convex,  as 
may  be  perceived  in  the  mercury  of  the  barometer  when 
rising.  The  absorption  of  moisture  by  sponges,  sugar, 
salt,  &c.,  are  familiar  examples  of  capillary  attraction. 
Indeed  the  pores  of  sugar  are  so  minute,  that  there 
seems  to  be  no  limit  to  the  ascent  of  the  liquid.  Wine 
is  drawn  up  in  a  curve  on  the  interior  surface  of  a  glass ; 
tea  rises  above  its  level  on  the  side  of  a  cup ;  but  if  the 
glass  or  cup  be  too  full,  the  edges  attract  the  liquid 
downward,  and  give  it  a  rounded  form.  A  column  of 
liquid  will  rise  above  or  sink  below  its  level  between  two 
plane  parallel  surfaces  when  near  to  one  another,  ac- 
cording to  the  relative  densities  of  the  plates  and  the 
liquid  (N.  171) ;  and  the  phenomena  will  be  exactly  the 
same  as  in  a  cylindrical  tube  whose  diameter  is  double 
the  distance  of  the  plates  from  each  other.  If  the  two 
surfaces  be  very  near  to  one  another,  and  touch  each 
other  at  one  of  their  upright  edges,  the  liquid  will  rise 
highest  at  the  edges  that  are  in  contact,  and  will  grad- 
ually diminish  in  height  as  the  surfaces  become  more 
separated.  The  whole  outline  of  the  liquid  column  will 
have  the  form  of  a  hyperbola.  Indeed  so  universal  is 
the  action  of  capillarity,  that  solids  and  liquids  cannot 
touch  one  another  without  producing  a  change  in  the 
form  of  the  surface  of  the  liquid. 


SBCT.  XV.  CAPILLARY  ATTRACTION.  Ill 

The  attractions  and  repulsions  arising  from  capillarity 
present  many  curious  phenomena.  If  two  plates  of 
glass  or  metal,  both  of  which  are  either  dry  or  wet,  be 
partly  immersed  in  a  liquid  parallel  to  one  another,  the 
liquid  will  be  raised  or  depressed  close  to  their  surfaces, 
but  will  maintain  its  level  through  the  rest  of  the  space 
that  separates  them.  At  such  a  distance  they  neither 
attract  nor  repel  one  another ;  but  the  instant  they  are 
brought  so  near  as  to  make  the  level  part  of  the  liquid 
disappear,  and  the  two  curved  parts  of  it  meet,  the  two 
plates  will  rush  toward  each  other  and  remain  pressed 
together  (N.  172).  If  one  of  the  surfaces  be  wet  and 
the  other  dry,  they  will  repel  one  another  when  so  near 
as  to  have  a  curved  surface  of  liquid  between  them  ;  but 
if  forced  to  approach  a  little  nearer  the  repulsion  will  be 
overcome,  and  they  will  attract  each  other  as  if  they 
were  both  wet  or  both  dry.  Two  balls  of  pith  or  wood 
floating  in  water,  or  two  balls  of  tin  floating  in  mercury, 
attract  one  another  as  soon  as  they  are  so  near  that  the 
surface  of  the  liquid  is  curved  between  them.  Two 
ships  in  the  ocean  may  be  brought  into  collision  by  this 
principle.  But  two  balls,  one  of  which  is  wet  and  the 
other  dry,  repel  one  another  as  soon  as  the  liquid  which 
separates  them  is  curved  at  its  surface.  A  bit  of  tea 
leaf  is  attracted  by  the  edge  of  the  cup  if  wet  and  re- 
pelled when  dry,  provided  it  be  not  too  far  from  the 
edge  and  the  cup  moderately  full ;  if  too  full,  the  con- 
trary takes  place.  It  is  probable  that  the  rise  of  the 
sap  in  vegetables  is  in  some  degree  owing  to  capillarity. 


SECTION  XV. 

Analysis  of  the  Atmosphere— Its  Pressure— Law  of  Decrease  in  Density- 
Law  of  Decrease  in  Temperature— Measurement  of  Heights  by  the 
Barometer— Extent  of  the  Atmosphere— Barometrical  Variations— Oscil- 
lations—Trade  Winds— Monsoons— Rotation  of  Winds— Laws  of  Hur- 
ricanes— Water-Spouts. 

THE  atmosphere  is  not  homogeneous.  It  appears 
from  analysis  that  of  100  parts  79  are  azotic  gas,  and  21 
oxygen,  the  great  source  of  combustion  and  animal  heat. 
Besides  these  there  are  three  or  four  parts  of  carh 


112  DENSITY  OF  THE  ATMOSPHERE.          SECT.  XV. 

acid  gas  in  1000  parts  of  atmospheric  air.  These  pro- 
portions are  found  to  be  the  same  at  all  heights  hitherto 
attained  by  man.  The  air  is  an  elastic  fluid  resisting 
pressure  in  every  direction,  and  is  subject  to  the  law  of 
gravitation.  As  the  space  in  the  top  of  the  tube  of  a 
barometer  is  a  vacuum,  the  column  of  mercury  sus- 
pended by  the  pressure  of  the  atmosphere  on  the  sur- 
face of  the  cistern  is  a  measure  of  its  weight.  Conse- 
quently every  variation  in  the  density  occasions  a  cor- 
responding rise  or  fall  in  the  barometrical  column.  The 
pressure  of  the  atmosphere  is  about  fifteen  pounds  on 
every  square  inch;  so  that  the  surface  of  the  whole 
globe  sustains  a  weight  of  11,449,000,000  hundreds  of 
millions  of  pounds.  Shell-fish  which  have  the  power  of 
producing  a  vacuum,  adhere  to  the  rocks  by  a  pressure 
of  fifteen  pounds  upon  every  square  inch  of  contact. 

Since  the  atmosphere  is  both  elastic  and  heavy,  its 
density  necessarily  diminishes  in  ascending  above  the 
surface  of  the  earth ;  for  each  stratum  of  air  is  com- 
pressed only  by  the  weight  above  it.  Therefore  the 
upper  strata  are  less  dense,  because  they  are  less  com- 
pressed than  those  below  them.  Whence  it  is  easy  to 
show,  supposing  the  temperature  to  be  constant,  that  if 
the  heights  above  the  earth  be  taken  in  increasing 
arithmetical  progression — that  is,  if  they  increase  by 
equal  quantities,  as  by  a  foot  or  a  mile,  the  densities  of 
the  strata  of  air,  or  the  heights  of  the  barometer  which 
are  proportionate  to  them,  will  decrease  in  geometrical 
progression.  For  example,  at  the  level  of  the  sea,  if  the 
mean  height  of  the  barometer  be  29-922  inches,  at  the 
height  of  18,000  feet  it  will  be  14-961  inches,  or  one 
half  as  great;  at  the  height  of  36,000  feet,  it  will  be  one 
fourth  as  great;  at  54,000  feet,  it  will  be  one  eighth, 
and  so  on,  which  affords  a  method  of  measuring  the 
heights  of  mountains  with  considerable  accuracy,  and 
would  be  very  simple,  if  the  decrease  in  the  density  of 
the  air  were  exactly  according  to  the  preceding  law. 
But  it  is  modified  by  several  circumstances,  and  chiefly 
by  changes  of  temperature,  because  heat  dilates  the 
air  and  cold  contracts  it,  varying  ¥]F  of  the  whole  bulk 
when  at  32°,  for  every  degree  of  Fahrenheit's  ther- 
mometer. Experience  shows  that  the  heat  of  the  air 


8«cr.  XV.         BAROMETRICAL  MEASUREMENTS.  113 

decreases  as  the  height  above  the  surface  of  the  earth 
increases.  And  it  appears  from  recent  investigations 
that  the  mean  temperature  of  space  is  58°  below  the 
zero  point  of  Fahrenheit,  which  would  probably  be  the 
temperature  of  the  surface  of  the  earth  also  were  it 
not  for  the  non-conducting  power  of  the  air,  whence  it 
is  enabled  to  retain  the  heat  of  the  sun's  rays,  which 
the  earth  imbibes  and  radiates  in  all  directions.  The 
decrease  in  heat  is  very  irregular ;  each  authority  gives 
a  different  estimate :  probably  because  the  decrease 
varies  with  the  latitude  as  well  as  the  height,  and  some- 
thing is  due  also  to  local  circumstances.  But  from  the 
mean  of  five  different  statements,  it  seems  to  be  about 
one  degree  for  every  334  feet,  which  is  the  cause  of  the 
severe  cold  and  eternal  snows  on  the  summits  of  the 
Alpine  chains.  Of  the  various  methods  of  computing 
heights  from  barometrical  measurements,  that  of  Mr. 
Ivory  has  the  advantage  of  combining  accuracy  with  the 
greatest  simplicity.  Indeed  the  accuracy  with  which 
the  heights  of  mountains  can  be  obtained  by  this  method 
is  very  remarkable.  Captain  Smyth,  R.N.,  and  Sir 
John  Herschel  measured  the  height  of  Etna  by  the 
barometer  without  any  communication  ^and  hi  different 
years;  Captain  Smyth  made  it  10,874  feet,  and  Sir  John 
Herschel  10,873 ;  the  difference  being  only  one  foot.  In 
consequence  of  the  diminished  pressure  of  the  atmos- 
phere, water  boils  at  a  lower  temperature  on  the  moun- 
tain tops  than  in  the  valleys,  which  induced  Fahrenheit 
to  propose  this  mode  of  observation  as  a  method  of  as- 
certaining then*  heights.  It  is  very  simple,  as  Professor 
Forbes  has  ascertained  that  the  temperature  of  the  boil- 
ing point  varies  in  an  arithmetical  proportion  with  the 
height,  or  549-5  feet  for  every  degree  of  Fahrenheit,  so 
that  the  calculation  of  height  becomes  one  of  arithmetic 
only  without  the  use  of  any  table. 

The  atmosphere  when  in  equilibrio  is  an  ellipsoid 
flattened  at  the  poles  from  its  rotation  with  the  earth. 
In  that  state  its  strata  are  of  uniform  density  at  equal 
heights  above  the  level  of  the  sea,  and  it  is  sensible  of 
finite  extent  when  it  consists  of  particles  infinitely  divisi- 
ble or  not.  On  the  latter  hypothesis  it  must  really  be 
finite,  and  even  if  its  particles  be  infinitely  divisible  it  is 
8  IL2 


114  EXTENT  OF  THE  ATMOSPHERE.  SECT.  XV. 

known  by  experience  to  be  of  extreme  tenuity  at  very 
small  heights.  The  barometer  rises  in  proportion  to 
the  super-incumbent  pressure.  At  the  level  of  the  sea 
in  the  latitude  of  45°  and  at  the  temperature  of  melting 
ice,  the  mean  height  of  the  barometer  being  29-922 
inches,  the  density  of  the  air  is  to  the  density  of  a  simi- 
lar volume  of  mercury  as  1  to  10477-9.  Consequently 
the  height  of  the  atmosphere  supposed  to  be  of  uniform 
density  would  be  about  4-95  miles.  But  as  the  density 
decreases  upward  in  geometrical  progression  it  is  consid- 
erably higher,  probably  about  fifty  miles  ;  at  that  height 
it  must  be  of  extreme  tenuity,  for  the  decrease  in  density 
is  so  rapid  that  three  fourths  of  all  the  air  contained  in 
the  atmosphere  is  within  four  miles  of  the  earth ;  and, 
as  its  superficial  extent  is  200  millions  of  square  miles, 
its  relative  thickness  is  less  than  that  of  a  sheet  of  paper 
when  compared  with  its  breadth.  The  air  even  on 
mountain  tops  is  sufficiently  rare  to  diminish  the  intensity 
of  sound,  to  affect  respiration,  and  to  occasion  a  loss  of 
muscular  strength.  The  blood  burst  from  the  lips  and 
ears  of  M.  de  Humboldt^as  he  ascended  the  Andes; 
and  he  experienced  the  same  difficulty  in  kindling  and 
maintaining  a  fire  at  great  heights  which  Marco  Polo 
the  Venetian  felt  on  the  mountains  of  Central  Asia.  M. 
Gay-Lussac  and  M.  Biot  ascended  in  a  balloon  to  the 
height  of  4-36  miles,  which  is  the  greatest  elevation  that 
man  has  attained,  and  they  suffered  greatly  from  the 
rarity  of  the  air.  It  is  true  that  at  the  height  of  thirty- 
seven  miles,  the  atmosphere  is  still  dense  enough  to 
reflect  the  rays  of  the  sun  when  18°  below  the  horizon  ; 
but  the  tails  of  comets  show  that  extremely  attenuated 
matter  is  capable  of  reflecting  light.  And  although,  at 
the  height  of  fifty  miles,  the  bursting  of  the  meteor  of 
1783  was  heard  on  earth  like  the  report  of  a  cannon,  it 
only  proves  the  immensity  of  the  explosion  of  a  mass 
half  a  mile  in  diameter,  which  could  produce  a  sound 
capable  of  penetrating  air  three  thousand  times  more 
rare  than  that  we  breathe.  But  even  these  heights  are 
extremely  small  when  compared  with  the  radius  of  the 
earth. 

The  mean  pressure  of  the  atmosphere  is  not  the  same 
all  over  the  globe.     It  is  less  at  the  equator  than  at  the 


SKCT.  XV.         ACTION  OP  THE  SUN  AND  MOON.  115 

tropics  or  in  the  higher  latitudes,  in  consequence  of  the 
ascent  of  the  heated  air  from  the  surface  of  the  earth  ; 
it  is  less  also  on  the  shores  of  the  Baltic  sea  than  it  is 
in  France,  probably  from  some  permanent  eddy  in  the 
air  arising  from  the  conformation  of  the  surrounding 
land ;  and  to  similar  local  causes  those  barometric  depres- 
sions may  be  attributed  which  have  been  observed  by 
M.  Erman,  near  the  Sea  of  Ochotzk  in  Eastern  Siberia, 
and  by  Captain  Foster  near  Cape  Horn. 

There  are  various  periodic  oscillations  in  the  atmos- 
phere which,  rising  and  falling  like  waves  in  the  sea, 
occasion  corresponding  changes  in  the  height  of  the 
barometer,  but  they  differ  as  much  from  the  trade  winds, 
monsoons,  and  other  currents,  as  the  tides  of  the  sea  do 
from  the  Gulf-stream  and  other  oceanic  rivers.  The 
sun  and  moon  disturb  the  equilibrium  of  the  atmosphere 
by  their  attraction,  and  produce  annual  undulations  which 
have  their  maximum  altitudes  at  the  equinoxes  and  their 
minima  at  the  solstices.  There  are  also  lunar  tides 
which  ebb  and  flow  twice  in  the  course  of  a  lunation. 
The  diurnal  tides,  which  accomplish  their  rise  and  fall 
in  six  hours,  are  greatly  modified  by  the  heat  of  the 
sun.  Between  the  tropics  the  barometer  attains  its 
maximum  height  about  nine  hi  the  morning,  then  sinks 
till  three  or  four  in  the  afternoon;  it  again  rises  and 
attains  a  second  maximum  about  nine  in  the  evening, 
and  then  it  begins  to  fall  and  reaches  a  second  minimum 
at  three  in  the  morning,  again  to  pursue  the  same  course. 
According  to  M.  Bouvard,  the  amount  of  the  oscillations 
at  the  equator  is  proportional  to  the  temperature,  and 
in  other  parallels  it  varies  as  the  temperature  and  the 
square  o'f  the  cosine  of  the  latitude  conjointly,  conse- 
quently it  decreases  from  the  equator  to  the  poles,  but 
it  is  somewhat  greater  in  the  day  than  in  the  night. 

Besides  these  small  undulations,  there  are  vast  waves 
perpetually  moving  over  the  continents  and  oceans  in 
separate  and  independent  systems,  being  confined  to 
local  yet  very  extensive  districts,  probably  occasioned  by 
long-continued  rains  or  dry  weather  over  large  tracts  of 
country.  By  numerous  barometrical  observations  made 
simultaneously  in  both  hemispheres,  the  courses  of  sev- 
eral have  been  traced,  some  of  which  occupy  twenty -four 


116  THE  TRADE;- WINDS.  SBCT.  xv. 

and  others  thirty-six  hours  to  accomplish  their  rise  and 
fall.  One  especially  of  these  vast  barometric  waves,  many 
hundreds  of  miles  in  breadth,  has  been  traced  over  the 
greater  part  of  Europe,  and  not  its  breadth  only,  but  also 
the  direction  of  its  front  and  its  velocity  have  been  clearly 
ascertained.  Although  like  ah1  other  waves  these  are 
but  moving  forms,  yet  winds  arise  dependent  on  them 
like  tide  streams  in  the  ocean.  Mr.  Birt  has  deter- 
mined the  periods  of  other  waves  of  still  greater  extent 
and  duration,  two  of  which  require  seventeen  days  to 
rise  and  fall,  and  another  took  thirteen  days  to  complete 
its  undulation.  Since  each  oscillation  has  its  perfect 
effect  independently  of  the  others,  each  one  is  marked 
by  a  change  in  the  barometer,  and  this  is  beautifully 
illustrated  by  curves  constructed  from  a  series  of  obser- 
vations. The  general  form  of  the  curve  shows  the 
course  of  the  principal  wave,  while  small  undulations  in 
its  outline  mark  the  maxima  and  minima  of  the  minor 
oscillations. 

The  trade-winds,  which  are  the  principal  currents  in 
the  atmosphere,  are  only  a  particular  case  of  those  very 
general  laws  which  regulate  the  motion  of  the  winds 
depending  on  the  rarefaction  of  the  air  combined  with 
the  rotation  of  the  earth  on  its  axis. 

The  heat  of  the  sun  occasions  these  ae'rial  currents 
by  rarefying  the  air  at  the  equator,  which  causes  the 
cooler  and  more  dense  part  of  the  atmosphere  to  rush 
along  the  surface  of  the  earth  from  the  poles  toward  the 
equator,  while  that  which  is  heated  is  carried  along  the 
higher  strata  to  the  poles,  forming  two  counter-currents 
in  the  direction  of  the  meridian.  But  the  rotatory  ve- 
locity of  the  air  corresponding  to  its  geographical  posi- 
tion decreases  toward  the  poles.  In  approaching  the 
equator  it  must  therefore  revolve  more  slowly  than  the 
corresponding  parts  of  the  earth,  and  the  bodies  on  the 
surface  of  the  earth  must  strike  against  it  with  the  ex- 
cess of  their  velocity,  and  by  its  reaction  they  will  meet 
with  a  resistance  contrary  to  their  motion  of  rotation. 
So  that  the  wind  will  appear  to  a  person  supposing  him- 
self to  be  at  rest,  to  blow  in  a  direction  nearly  though 
not  altogether  contrary  to  the  earth's  rotation ;  because 
these  currents  will  still  retain  a  part  of  their  northerly 


SicT.  XV.  THE  TRADE-WINDS.  117 

and  southerly  impetus,  which,  combining  with  their  de- 
ficiency of  rotatory  velocity,  will  make  them  appear  to 
blow  from  the  north-east  on  one  side  of  the  equator  and 
from  the  south-east  on  the  other,  which  is  the  general 
direction  of  the  trade-winds.  But  they  are  modified 
both  hi  intensity  and  direction  by  the  seasons,  by  the 
neighborhood  of  continents,  and  by  the  nature  of  the 
soil,  so  that  the  phenomena  are  not  the  same  in  both 
hemispheres.  These  winds,  however,  are  not  felt  at  all 
under  the  line,  because  the  easterly  tendency  of  the 
two  great  polar  currents  is  gradually  diminished  as  they 
approach  the  equator  by  the  friction  of  the  earth,  which 
slowly  imparts  a  portion  of  its  rotatory  velocity  to  them 
as  they  pass  along,  and  when  they  meet  in  the  equator 
they  destroy  one  another's  impetus.  The  equator  does 
not  exactly  coincide  with  the  line  which  separates  the 
trad^-winds  north  and  south  of  it.  That  line  of  separa- 
tion depends  upon  the  total  difference  of  heat  in  the  two 
hemispheres,  arising  from  the  distribution  of  land  and 
water,  and  other  causes. 

The  polar  currents  from  defect  of  rotatory  velocity 
tend,  by  their  friction  near  the  equator,  tor  diminish  the 
velocity  of  the  earth's  rotation  ;  while,  on  the  contrary, 
the  equatorial  or  upper  currents  carry  their  excess  of 
rotatory  velocity  north  and  south.  And  as  they  occa- 
sionally come  to  the  surface  in  their  passage  to  the  poles, 
they  act  on  the  earth  by  their  friction  as  a  strong  south- 
west wind  in  the  northern  hemisphere,  and  as  a  north- 
west wind  in  the  southern.  In  this  manner  the  equili- 
brium of  rotation  is  maintained.  Sir  John  Herschel 
ascribes  to  this  cause  the  western  and  south-western 
gales  so  prevalent  in  our  latitudes,  and  also  the  west 
winds  which  are  so  constant  in  the  North  Atlantic. 

There  are  many  proofs  of  the  existence  of  the  coun- 
ter-currents above  the  trade-winds.  On  the  Peak  of 
Teneriffe  the  prevailing  winds  are  from  the  west.  The 
ashes  of  the  volcano  of  St.  Vincent's,  in  the  year  1812, 
were  carried  to  windward  as  far  as  Barbadoes  by  the 
upper  current.  The  captain  of  a  Bristol  ship  declared 
that  on  that  occasion  dust  from  St.  Vincent's  fell  to  the 
depth  of  five  inches  on  the  deck  at  the  distance  of  500 
miles  to  the  eastward.  Light  clouds  have  frequently 


118  THE  MONSOONS.  SKCT.  XV. 

been  seen  moving  rapidly  from  west  to  east,  at  a  very 
great  height  above  the  trade-winds,  which  were  sweep- 
ing along  the  surface  of  the  ocean  in  a  contrary  direc- 
tion. Rains,  clouds,  and  nearly  all  the  other  atmos- 
pheric phenomena  occur  below  the  height  of  18,000 
feet,  and  generally  much  nearer  to  the  surface  of  the 
earth.  They  are  owing  to  currents  of  air  running  upon 
each  other  in  horizontal  strata,  and  differing  in  their 
electric  state,  in  temperature  and  moisture,  as  well  as 
in  velocity  and  direction. 

The  monsoons  are  steady  currents  six  months  in  du- 
ration, owing  to  diminished  atmospheric  pressure  at  each 
tropic  alternately  from  the  heat  of  the  sun,  thereby  pro- 
ducing a  regular  alternation  of  north  and  south  winds, 
which  combining  their  motion  with  that  of  the  earth  on 
its  axis  become  a  north-east  wind  in  the  northern  hem- 
isphere and  a  south-west  in  the  southern  ;  the  former 
blows  from  April  to  October  and  the  latter  from  October 
to  April.  The  change  from  one  to  the  other  is  at- 
tended by  violent  rains,  with  storms  of  thunder  and 
lightning.  From  some  peculiar  conformation  of  the 
land  and  water,  these  winds  are  confined  to  the  Arabian 
Gulf,  the  Indian  Ocean,  and  the  China  Sea. 

When  north  and  south  winds  blow  alternately,  the 
wind  at  any  place  will  veer  in  one  uniform  direction 
through  every  point  of  the  compass,  provided  the  one 
begins  before  the  other  has  ceased.  In  the  northern 
hemisphere  a  north  wind  sets  out  with  a  smaller  degree 
of  rotatory  motion  than  the  places  have  at  which  it  suc- 
cessively arrives,  consequently  it  passes  through  all  the 
points  of  the  compass  from  N.  to  N.  E.  and  E.  A  cur- 
rent from  the  south,  on  the  contrary,  sets  out  with  a 
greater  rotatoiy  velocity  than  the  places  have  at  which 
it  successively  arrives,  so  by  the  rotation  of  the  earth  it 
is  deflected  from  S.  to  S.  W.  and  W.  Now  if  the  vane 
at  any  place  should  have  veered  from  the  N.  through 
N.  E.  to  E.r  and  a  south  wind  should  spring  up,  it  would 
combine  its  motion  with  the  former  and  cause  the  vane 
to  turn  successively  from  the  E.  to  S.  E.  and  S.  But 
by  the  earth's  rotation  this  south  wind  will  veer  to  the 
S.  W.  and  W.,  and  if  a  north  wind  should  now  arise,  it 
would  combine  its  motion  with  that  of  the  west  and 


SBCT.  XV.  HURRICANES.  119 

cause  it  to  veer  to  the  N.  W.  and  N.  Thus  two  alter- 
nations of  north  and  south  wind  will  cause  the  vane  at 
any  place  to  go  completely  round  the  compass,  from  N. 
to  E.,  S.,  W.,  and  N.  again.  At  the  Royal  Observatory 
at  Greenwich,  the  wind  accomplishes  five  circuits  in  that 
direction  in  the  course  of  a  year.  When  circumstances 
combine  to  produce  alternate  north  and  south  winds  in 
the  southern  hemisphere,  the  gyration  is  in  the  contrary 
direction.  Although  the  general  tendency  of  the  wind 
may  be  rotatoiy,  and  is  so  in  many  instances,  at  least 
for  part  of  the  year,  yet  it  is  so  often  counteracted  by 
local  circumstances,  that  the  winds  are  in  general  very 
irregular  ;  every  disturbance  in  atmospheric  equilibrium 
from  heat  or  any  other  cause  producing  a  corresponding 
wind.  The  most  prevalent  winds  in  Europe  are  the 
N.  E.  and  S.  W. ;  the  former  arises  from  the  north 
polar  current,  and  the  latter  from  causes  already  men- 
tioned. The  law  of  the  wind's  rotation  was  noticed  by 
Dr.  Dalton,  but  has  been  developed  by  Professor  Dove, 
of  Berlin. 

Hurricanes  are  those  storms  of  wind  in  which  the 
portion  of  the  atmosphere  that  forms  them  revolves  in  a 
horizontal  circuit  round  a  vertical  or  somewhat  inclined 
axis  of  rotation,  while  the  axis  itself,  and  consequently 
the  whole  storm,  is  carried  forward  along  the  surface  of 
the  globe,  so  that  the  direction  in  which  the  storm  is 
advancing  is  quite  different  from  the  direction  in  which 
the  rotatory  current  may  be  blowing  at  any  point.  In 
the  West  Indies,  where  hurricanes  are  frequent  and 
destructive,  they  generally  originate  in  the  tropical 
regions  near  the  inner  boundary  of  the  trade-winds,  and 
are  probably  owing  to  a  portion  of  the  superior  current 
of  wind  penetrating  through  the  lower.  By  far  the 
greater  number  of  Atlantic  hurricanes  have  begun 
eastward  of  the  lesser  Antilles  or  Caribbean  Islands. 

In  every  case  the  axis  of  the  storm  moves  in  an 
elliptical  or  parabolic  curve,  having  its  vertex  hi  or  near 
the  tropic  of  Cancer,  which  marks  the  external  limit  of 
the  trade-winds  north  of  the  equator.  As  the  motion 
before  it  reaches  the  tropic  is  in  a  straight  line  from  S. 
E.  to  N.  W.,  and  after  it  has  passed  it  from  S.  W.  to 
N.  E.,  the  bend  of  the  curve  is  turned  toward  Florida 


120  HURRICANES.  SECT.  XV. 

and  the  Carolinas.  In  the  southern  hemisphere  the 
body  of  the  storms  moves  in  exactly  the  opposite  direc- 
tion. The  hurricanes  which  originate  south  of  the 
equator,  and  whose  initial  path  is  from  N.  E.  to  S.  W., 
bend  round  at  the  tropic  of  Capricorn,  and  then  bend 
from  N.  W.  to  S.  E. 

The  extent  and  velocity  of  these  storms  are  great ; 
for  instance,  the  hurricane  that  took  place  on  the  12th 
of  August,  1830,  was  traced  from  the  eastward  of  the 
Caribbee  Islands  to  the  bank  of  Newfoundland,  a  distance 
of  more  than  3000  miles,  which  it  passed  over  in  six 
days.  Although  the  hurricane  of  the  1st  of  September, 
1821,  was  not  so  extensive,  its  velocity  was  greater,  as 
it  moved  at  the  rate  of  30  miles  an  hour :  small  storms 
are  generally  more  rapid  than  those  of  greater  dimen- 
sions. 

The  action  of  these  storms  seems  to  be  at  first  con- 
fined to  the  stratum  of  air  nearest  the  earth,  and  then 
they  seldom  appear  to  be  more  than  a  mile  high, 
though  sometimes  they  are  raised  higher ;  or  even 
divided  by  a  mountain  into  two  separate  storms,  each  of 
which  continues  its  new  path  and  gyrations  with  in- 
creased violence.  This  occurred  in  the  gale  of  the  25th 
of  December,  1821,  in  the  Mediterranean,  when  the 
Spanish  mountains  and  the  Maritime  Alps  became  new 
centers  of  motion. 

By  the  friction  of  the  earth  the  axis  of  the  storm 
bends  a  little  forward,  so  that  the  whirling  motion  begins 
in  the  higher  regions  of  the  atmosphere  before  it  is  felt 
on  the  earth.  This  causes  a  continual  intermixture  ot 
the  lower  and  warmer  strata  of  air  with  those  that  are 
higher  and  colder,  producing  torrents  of  rain  and  violent 
electric  explosions. 

The  rotation  is  different  in  direction  in  different  hemi- 
spheres, though  always  alike  in  the  same.  In  the 
northern  hemisphere  the  gyration  is  contrary  to  the 
movement  of  the  hands  of  a  watch,  that  is  to  say,  the 
wind  revolves  from  east  round  through  the  north  to  the 
west,  south  and  east  again  ;  while  in  the  southern  hemi- 
sphere, the  rotation  about  the  axis  of  the  storm  is  in  the 
contrary  direction. 

The  breadth  of  the  whirlwind  is  greatly  augmented 


8«cr.  XV.  HURRICANES.  121 

when  the  path  of  the  storm  changes  on  crossing  the 
tropic.  The  vortex  of  a  storm  has  covered  an  extent  of 
the  surface  of  the  globe  500  miles  in  diameter. 

The  revolving  motion  accounts  for  the  sudden  and 
violent  changes  observed  during  hurricanes.  In  conse- 
quence of  the  rotation  of  the  air,  the  wind  blows  in  op- 
posite directions  on  each  side  of  the  axis  of  the  storm, 
and  the  violence  of  the  blast  increases  from  the  circum- 
ference toward  the  center  of  gyration,  but  hi  the  center 
itself  the  ah-  is  in  repose  :  hence,  when  the  body  of  the 
storm  passes  over  a  place,  the  wind  begins  to  blow  mod- 
erately, and  increases  to  a  hurricane  as  the  center  of 
the  whirlwind  approaches ;  then,  in  a  moment,  a  dead 
and  awful  calm  succeeds,  suddenly  followed  by  a  re- 
newal of  the  storm  in  all  its  violence,  but  now  blowing 
in  a  direction  diametrically  opposite  to  its  former  course. 
This  happened  at  the  Island  of  St.  Thomas,  on  the  2d 
of  August,  1837,  where  the  hurricane  increased  in  vio- 
lence till  half-past  seven  in  the  morning,  when  perfect 
stillness  took  place  for  forty  minutes,  after  which  the 
storm  recommenced  in  a  contrary  direction. 

The  sudden  fell  of  the  mercury  in  the  barometer  in 
the  regions  habitually  visited  by  hurricanes  is  a  certain 
indication  of  a  coming  tempest.  In  consequence  of  the 
centrifugal  force  of  these  rotatory  storms  the  air  be- 
comes rarefied,  and  as  the  atmosphere  is  disturbed  to 
some  distance  beyond  the  actual  circle  of  gyration  or 
limits  of  the  storm,  the  barometer  often  sinks  some 
hours  before  its  arrival,  from  the  original  cause  of  the 
rotatory  disturbance.  It  continues  sinking  under  the 
first  half  of  the  hurricane,  and  again  rises  during  the 
passage  of  the  latter  half,  though  it  does  not  attain  its 
greatest  height  till  the  storm  is  over.  The  diminution 
of  atmospheric  pressure  i§  greater  and  extends  over  a 
wider  area  in  the  temperate  zones  than  in  the  torrid, 
on  account  of  the  sudden  expansion  of  the  circle  of  rota- 
tion when  the  gale  crosses  the  tropic. 

As  the  fall  of  the  barometer  gives  warning  of  the  ap- 
proach of  a  hurricane,  so  the  laws  of  the  storm's  mo- 
tion afford  to  the  seaman  the  knowledge  to  guide  him  in 
avoiding  it.  In  the  northern  temperate  zone,  if  the  gale 
begins  from  the  S.  E.  and  veers  by  S.  to  W.,  the  ship 
L 


136  THEORY  OF  SOUND.  SECT.  XVI 

should  steer  to  the  S.  E. ;  but  if  the  gale  begins  from 
the  N.  E.,  and  changes  through  N.  to  N.  W.,  the  ves- 
sel should  go  to  the  N.  W.  In  the  northern  part  of  the 
torrid  zone,  if  the  storm  begin  from  the  N.  E.  and  veer 
through  E.  to  S.  E.,  the  ship  should  steer  to  the  N.  E. ; 
but  if  it  begin  from  the  N.  W.  and  veer  by  W.  to  S.  W., 
the  ship  should  steer  to  the  S.  W.,  because  she  is  in  the 
south-western  side  of  the  storm.  Since  the  laws  of 
storms  are  reversed  in  the  southern  hemisphere,  the 
rules  for  steering  vessels  are  necessarily  reversed  also. 
A  heavy  swell  is  peculiarly  characteristic  of  these 
storms.  In  the  open  sea  the  swell  often  extends  many 
leagues  beyond  the  range  of  the  gale  which  produced  it. 
Waterspouts  are  occasioned  by  small  whirlwinds, 
which  always  have  their  origin  at  a  great  distance  from 
that  part  of  the  sea  from  which  the  spout  begins  to  rise, 
where  it  is  generally  calm.  The  whirl  of  the  air  be- 
gins in  the  clouds,  and  extending  downward  to  the  sea, 
causes  the  water  to  ascend  in  a  spiral  by  the  impulse  of 
the  centrifugal  force.  When  waterspouts  have  a  pro- 
gressive motion,  the  vortex  of  air  in  the  cloud  above 
must  move  with  the  same  velocity,  otherwise  the  spouts 
break,  which  frequently  happens. 


SECTION  XVI. 

Sound — Propagation  of  Sound  illustrated  by  a  Field  of  Standing  Corn — 
Nature  of  Waves — Propagation  of  Sound  through  the  Atmosphere — 
Intensity  —  Noises  —  A  Musical  Sound  —  Quality  —  Pitch  —  Extent  of 
Human  Hearing — Velocity  of  Sound  in  Air,  Water,  and  Solids — Causes 
of  the  Obstruction  of  Sound — Law  of  its  Intensity — Reflection  of  Sound 
— Echoes — Thunder — Refraction  of  Sound — Interference  of  Sounds. 

ONE  of  the  most  important  uses  of  the  atmosphere  is 
the  conveyance  of  sound.  Without  the  air  deathlike 
silence  would  prevail  through  nature,  for  in  common 
with  all  substances  it  has  a  tendency  to  impart  vibrations 
to  bodies  in  contact  with  it.  Therefore  undulations  re- 
ceived by  the  air,  whether  it  be  from  a  sudden  impulse 
such  as  an  explosion  or  the  vibrations  of  a  musical  chord, 
are  propagated  in  every  direction,  and  produce  the  sen- 
sation of  sound  upon  the  auditory  nerves.  A  bell  rung 
under  the  exhausted  receiver  of  an  air-pump  is  inaudi- 


S«CT.  XVI.  UNDULATIONS  OF  OOBN.  123 

ble,  which  shows  that  the  atmosphere  is  really  the  me- 
dium of  sound.  In  the  small  undulations  of  deep  water 
in  a  calm,  the  vibrations  of  the  liquid  particles  are  made 
m  the  vertical  plane,  that  is  up  and  down,  or  at  right 
angles  to  the  direction  of  the  transmission  of  the  waves. 
But  the  vibrations  of  the  particles  of  ah*  which  produce 
sound  differ  from  these,  being  performed  in  the  same 
direction  in  which  the  waves  of  sound  travel.  The 
propagation  of  sound  has  been  illustrated  by  a  field  of 
corn  agitated  by  the  wind.  However  irregular  the 
motion  of  the  corn  may  seem  on  a  superficial  view,  it 
will  be  found,  if  the  velocity  of  the  wind  be  constant, 
that  the  waves  are  all*  precisely  similar  and  equal,  and 
that  all  are  separated  by  equal  intervals  and  move  in 
equal  times. 

A  sudden  blast  depresses  each  ear  equally  and  suc- 
cessively in  the  direction  of  the  wind,  but  in  conse- 
quence of  the  elasticity  of  the  stalks  and  the  force  of 
the  impulse,  each  ear  not  only  rises  again  as  soon  as 
the  pressure  is  removed,  but  bends  back  nearly  as 
much  in  the  contrary  direction,  and  then  continues  to 
oscillate  backward  and  forward  in  equal  times,  like  a 
pendulum  to  a  less  and  less  extent,  till  the  resistance  of 
the  air  puts  a  stop  to  the  motion.  These  vibrations  are 
the  same  for  every  individual  ear  of  corn.  Yet  as  their 
oscillations  do  not  all  commence  at  the  same  time,  but 
successively,  the  ears  will  have  a  variety  of  positions  at 
any  one  instant.  Some  of  the  advancing  ears  will  meet 
others  in  their  returning  vibrations,  and  as  the  times  of 
oscillation  are  equal  for  all,  they  will  be  crowded  to- 
gether at  regular  intervals.  Between  these  there  will 
occur  equal  spaces,  where  the  ears  will  be  few,  in  con- 
sequence of  being  bent  in  opposite  directions ;  and  at 
other  equal  intervals  they  will  be  in  their  natural  upright 
positions.  So  that  over  the  whole  field  there  will  be  a 
regular  series  of  condensations  and  rarefactions  among 
the  ears  of  corn,  separated  by  equal  intervals  where 
they  will  be  in  their  natural  state  of  density.  In  con- 
sequence of  these  changes  the  field  will  be  marked  by 
an  alternation  of  bright  and  dark  bands.  Thus  the 
successive  waves  which  fly  over  the  corn  with  the 
speed  of  the  wind,  are  totally  distinct  from,  and  entirely 


134  UNDULATIONS  OF  THE  AIR.  SECT.  XVI. 

independent  of  the  extent  of  the  oscillations  of  each  in- 
dividual ear,  though  both  take  place  in  the  same  direc- 
tion. The  length  of  a  wave  is  equal  to  the  space  be- 
tween two  ears  precisely  in  the  same  state  of  motion, 
or  which  are  moving  similarly,  and  the  time  of  the  vi- 
bration of  each  ear  is  equal  to  that  which  elapses  be- 
tween the  arrival  of  two  successive  waves  at  the  same 
point.  The  only  difference  between  the  undulations  of 
a  corn-field  and  those  of  the  air  which  produce  sound 
is,  that  each  ear  of  corn  is  set  in  motion  by  an  external 
cause  and  is  uninfluenced  by  the  motion  of  the  rest ; 
whereas  in  air,  which  is  a  compressible  and  elastic  fluid, 
when  one  particle  begins  to  oscillate,  it  communicates 
its  vibrations  to  the  surrounding  particles,  which  trans- 
mit them  to  those  adjacent,  and  so  on  continually. 
Hence  from  the  successive  vibrations  of  the  particles  of 
air  the  same  regular  condensations  and  rarefactions  take 
place  as  in  the  field  of  corn,  producing  waves  through- 
out the  whole  mass  of  air,  though  each  molecule,  like 
each  individual  ear  of  corn,  never  moves  far  from  its 
state  of  rest.  The  small  waves  of  a  liquid  and  the  un- 
dulations of  the  air  like  waves  in  the  corn,  are  evidently 
not  real  masses  moving  in  the  direction  in  which  they 
are  advancing,  but  merely  outlines,  motions,  or  forms 
passing  along,  and  comprehending  all  the  particles  of  an 
undulating  fluid  which  are  at  once  in  a  vibratory  state. 
It  is  thus  that  an  impulse  given  to  any  one  point  of  the 
atmosphere  is  successively  propagated  in  all  directions, 
in  a  wave  diverging  as  from  the  center  of  a  sphere  to 
greater  and  greater  distances,  but  with  decreasing  in- 
tensity, in  consequence  of  the  increasing  number  of  par- 
ticles of  inert  matter  which  the  force  has  to  move  ;  like 
the  waves  formed  in  still  water  by  a  falling  stone,  which 
are  propagated  circularly  all  around  the  center  of'  dis- 
turbance (N.  156). 

The  intensity  of  sound  depends  upon  the  violence 
and  extent  of  the  initial  vibrations  of  air ;  but  whatever 
they  may  be,  each  undulation  when  once  formed  can 
only  be  transmitted  straight  forward,  and  never  returns 
back  again  unless  when  reflected  by  an  opposing  ob- 
stacle. The  vibrations  of  the  aSrial  molecules  are  al- 
ways extremely  small,  whereas  the  waves  of  sound 


.  XVI.  EXTENT  OP  HEARING.  125 

vary  from  a  few  inches  to  several  feet.  The  various 
musical  instruments,  the  human  voice  and  that  of  ani- 
mals, the  singing  of  birds,  the  hum  of  insects,  the  roar 
of  the  cataract,  the  whistling  of  the  wind,  and  the  other 
nameless  peculiarities  of  sound,  show  at  once  an  infinite 
variety  in  the  modes  of  ae'rial  vibration,  and  the  aston- 
ishing acuteness  and  delicacy  of  the  ear,  thus  capable  of 
appreciating  the  minutest  differences  in-  the  laws  of 
molecular  oscillation. 

All  mere  noises  are  occasioned  by  irregular  impulses 
communicated  to  the  ear,  and  if  they  be  short,  sudden, 
and  repeated  beyond  a  certain  degree  of  quickness,  the 
ear  loses  the  intervals  of  silence  and  the  sound  appears 
continuous.  Still  such  sounds  will  be  mere  noise:  in 
order  to  produce  a  musical  sound,  the  impulses,  and 
consequently  the  undulations  of  the  air  must  be  all  ex- 
nctly  similar  in  duration  and  intensity,  and  must  recur 
after  exactly  equal  intervals  of  time.  If  a  blow  be  given 
to  the  nearest  of  a  series  of  broad,  flat,  and  equidistant 
palisades  set  edgewise  in  a  line  direct  from  the  ear, 
each  palisade  will  repeat  or  echo  the  sound ;  and  these 
echoes  returning  to  the  ear  at  successive  equal  intervals 
of  time  will  produce  a  musical  note.  The  quality  of  a 
musical  note  depends  upon  the  abruptness,  and  its  in- 
tensity upon  the  violence  and  extent  of  the  original  im- 
pulse. In  the  theory  of  harmony  the  only  property  of 
sound  taken  into  consideration  is  the  pitch,  which  varies 
with  the  rapidity  of  the  vibrations.  The  grave  or  low 
tones  are  produced  by  very  slow  vibrations,  which  in- 
crease in  frequency  as  the  note  becomes  more  acute. 
Very  deep  tones  are  not  heard  by  all  alike,  and  Dr.  Wol- 
laston,  who  made  a  variety  of  experiments  on  the  sense 
of  hearing,  found  that  many  people  though  not  at  all 
deaf  are  quite  insensible  to  the  cry  of  the  bat  or  the 
cricket,  while  to  others  it  is  painfully  shrill.  From  his 
experiments  he  concluded  that  human  hearing  is  limited 
to  about  nine  octaves,  extending  from  the  lowest  note  of 
the  organ  to  the  highest  known  cry  of  insects ;  and  he 
observes  with  his  usual  originality  that,  "  as  there  is 
nothing  in  the  nature  of  the  atmosphere  to  prevent  the 
existence  of  vibrations  incomparably  more  frequent  than 
any  of  which  we  are  conscious,  we  may  imagine  that 
1,2 


126  EXPERIMENTS  OP  M.  SAVART.  SKCT.  XVI. 

animals  like  the  Grylli,  whose  powers  appear  to  com- 
mence nearly  where  ours  terminate,  may  have  the  fac- 
ulty of  hearing  still  sharper  sounds  which  we  do  not 
know  to  exist,  and  that  there  may  be  other  insects  hear- 
ing nothing  in  common  with  us,  but  endowed  with  a 
power  of  exciting,  and  a  sense  which  perceives  vibrations 
of  the  same  nature  indeed  as  those  which  constitute  our 
ordinary  sounds,  but  so  remote  that  the  animals  who 
perceive  them  may  be  said  to  possess  another  sense, 
agreeing  with  our  own  solely  in  the  medium  by  which 
it  is  excited. 

M.  Savart,  so  well  known  for  the  number  and  beauty 
of  his  researches  in  acoustics,  has  proved  that  a  high 
note  of  a  given  intensity  being  heard  by  some  ears  and 
not  by  others,  must  not  be  attributed  to  its  pitch,  but  to 
its  feebleness.  His  experiments,  and  those  more  re- 
cently made  by  Professor  Wheatstone,  show,  that  if  the 
pulses  could  be  rendered  sufficiently  powerful,  it  would 
be  difficult  to  fix  a  limit  to  human  hearing  at  either  end 
of  the  scale.  M.  Savart  had  a  wheel  made  about  nine 
inches  in  diameter  with  360  teeth  set  at  equal  distances 
round  its  rim,  so  that  while  in  motion  each  tooth  suc- 
cessively hit  on  a  piece  of  card.  The  tone  increased  in 
pitch  with  the  rapidity  of  the  rotation,  and  was  very 
pure  when  the  number  of  strokes  did  not  exceed  three 
or  four  thousand  in  a  second,  but  beyond  that  it  became 
feeble  and  indistinct.  With  a  wheel  of  a  larger  size  a 
much  higher  tone  could  be  obtained,  because  the  teeth 
being  wider  apart  the  blows  were  more  intense  and 
more  separated  from  one  another.  With  720  teeth  on 
a  wheel  thirty-two  inches  in  diameter,  the  sound  pro- 
duced by  12,000  strokes  in  a  second  was  audible,  which 
corresponds  to  24,000  vibrations  of  a  musical  chord.  So 
that  the  human  ear  can  appreciate  a  sound  which  only 
lasts  the  24,000th  part  of  a  second.  This  note  was  dis- 
tinctly heard  by  M.  Savart  and  by  several  people  who 
were  present,  which  convinced  him  that  with  another 
apparatus  still  more  acute  sounds  might  be  rendered 
audible. 

For  the  deep  tones  M.  Savart  employed  a  bar  of  iron, 
two  feet  eight  inches  long,  about  two  inches  broad,  and 
half  an  inch  in  thickness,  which  revolved  about  its  center 


SECT.  XVI.  VELOCITY  OF  SOUND.  127 

as  if  its  arms  were  the  spokes  of  a  wheel.  When  such 
a  machine  rotates  it  impresses  a  motion  on  the  air  simi- 
lar to  its  own,  and  when  a  thin  board  or  card  is  brought 
close  to  its  extremities,  the  current  of  air  is  moment- 
arily interrupted  at  the  instant  each  arm  of 'the  bar 
passes  before  the  card ;  it  is  compressed  above  the  card 
and  dilated  below  ;  but  the  instant  the  spoke  has  passed, 
a  rush  of  ah*  to  restore  equilibrium  makes  a  kind  of  ex- 
plosion, and  when  these  succeed  each  other  rapidly,  a 
musical  note  is  produced  of  a  pitch  proportional  to  the 
velocity  of  the  revolution.  When  M.  Savart  turned  this 
bar  slowly  a  succession  of  single  beats  was  heard ;  as 
the  velocity  became  greater  the  sound  was  only  a  rattle ; 
but  as  soon  as  it  was  sufficient  to  give  eight  beats  in  a 
second,  a  very  deep  musical  note  was  distinctly  audible, 
corresponding  to  sixteen  single  vibrations  in  a  second, 
which  is  the  lowest  that  has  hitherto  been  produced. 
When  the  velocity  of  the  bar  was  much  increased  the 
intensity  of  the  sound  was  hardly  bearable.  The  spokes 
of  a  revolving  wheel  produce  the  sensation  of  sound,  on 
the  very  same  principle  that  a  burning  stick  whirled 
round  gives  the  impression  of  a  luminous  circle.  The 
vibrations  excited  in  the  organ  of  hearing  by  one  beat 
have  not  ceased  before  another  impulse  is  given.  In- 
deed it  is  indispensable  that  the  impressions  made  upon 
the  auditory  nerves  should  encroach  upon  each  other  in 
order  to  produce  a  full  and  continued  note.  On  the 
whole,  M.  Savart  has  come  to  the  conclusion,  that  the 
most  acute  sounds  would  be  heard  with  as  much  ease 
as  those  of  a  lower  pitch,  if  the  duration  of  the  sensation 
produced  by  each  pulse  could  be  diminished  proportion- 
ally to  the  augmentation  of  the  number  of  pulses  in  a 
given  time  :  and  on  the  contrary,  if  the  duration  of  the 
sensation  produced  by  each  pulse  could  be  increased  in 
proportion  to  their  number  in  a  given  time,  that  the 
deepest  tones  would  be  as  audible  as  any  of  the  others. 

The  velocity  of  sound  is  uniform  and  independent  of 
the  nature,  extent,  and  intensity  of  the  primitive  dis- 
turbance. Consequently  sounds  of  every  quality  and 
pitch  travel  with  equal  speed.  The  smallest  difference 
in  their  velocity  is  incompatible  either  with  harmony  or 
melody,  for  notes  of  different  pitches  and  intensities 


128  VELOCITY  OP  SOUND  SECT.  XVI 

sounded  together  at  a  little  distance,  would  arrive  at  the 
ear  in  different  times.  A  rapid  succession  of  notes 
would  in  this  case  produce  confusion  and  discord.  But 
as  the  rapidity  with  which  sound  is  transmitted  depends 
upon  the  elasticity  of  the  medium  through  which  it  has 
to  pass,  whatever  tends  to  increase  the  elasticity  of  the 
air  must  also  accelerate  the  motion  of  sound.  On  that 
account  its  velocity  is  greater  in  warm  than  in  cold 
weather,  supposing  the  pressure  of  the  atmosphere  con- 
stant. In  dry  air  at  the  freezing  temperature,  sound 
travels  at  the  rate  of  1090  feet  in  a  second,  and  for  any 
higher  temperature  one  foot  must  be  added  for  every 
degree  of  the  thermometer  above  32°  ;  hence  at  62°  of 
Fahrenheit  its  speed  in  a  second  is  1120  feet,  or  765 
miles  an  hour,  which  is  about  three-fourths  of  the  diur- 
nal velocity  of  the  earth's  equator.  Since  all  the  phe- 
nomena of  the  transmission  of  sound  are  simple  conse- 
quences of  the  physical  properties  of  the  air,  they  have 
been  predicted  and  computed  rigorously  by  the  laws  of 
mechanics.  It  was  found,  however,  that  the  velocity  of 
sound  determined  by  observation,  exceeded  what  it  ought 
to  have  been  theoretically  by  173  feet,  or  about  one-sixth 
of  the  whole  amount.  La  Place  suggested  that  this  dis- 
crepancy might  arise  from  the  increased  elasticity  of  the 
air  in  consequence  of  a  development  of  latent  heat  (N. 
173)  during  the  undulations  of  sound,  and  calculation 
confirmed  the  accuracy  of  his  views.  The  ae'rial  mole- 
cules being  suddenly  compressed  give  out  their  latent 
heat ;  and  as  air  is  too  bad  a  conductor  to  carry  it  rap- 
idly off,  it  occasions  a  momentary  and  local  rise  of  tem- 
perature which,  increasing  the  elasticity  of  the  air 
without  at  the  same  time  increasing  its  inertia,  causes 
the  movement  to  be  propagated  more  rapidly.  Analysis 
gives  the  true  velocity  of  sound  in  terms  of  the  elevation 
of  temperature  that  a  mass  of  air  is  capable  of  commu- 
nicating to  itself,  by  the  disengagement  of  its  own  latent 
heat  when  suddenly  compressed  in  a  given  ratio.  This 
change  of  temperature  however  could  not  be  obtained 
directly  by  any  experiments  which  had  been  made  at 
that  epoch ;  but  by  inverting  the  problem  and  assuming 
the  velocity  of  sound  as  given  by  experiment,  it  was 
computed  that  the  temperature  of  a  mass  of  air  is  raised 


SICT.  XVI.  TRANSMISSION  OF  SOUND.  129 

nine-tenths  of  a  degree  when  the  compression  is  equal 
to  j-}T  of  its  volume. 

Probably  all  liquids  are  elastic,  though  considerable 
force  is  required  to  compress  them.  Water  suffers  a 
condensation  of  nearly  0-0000496  for  every  atmosphere 
of  pressure,  and  is  consequently  capable  of  conveying 
sound  even  more  rapidly  than  air,  the  velocity  in  the  for- 
mer being  4708  feet  in  a  second.  A  person  under  water 
hears  sounds  made  in  air  feebly,  but  those  produced  in 
water  very  distinctly.  According  to  the  experiments  of 
M.  Colladon,  the  sound  of  a  bell  was  conveyed  under 
water  through  the  Lake  of  Geneva  to  the  distance  of 
about  nine  miles.  He  also  perceived  that  the  progress 
of  sound  through  water  is  greatly  impeded  by  the  inter- 
position of  any  object,  such  as  a  projecting  wall ;  conse- 
quently sound  under  water  resembles  light  hi  having  a 
distinct  shadow.  It  has  much  less  in  air,  being  trans- 
mitted all  round  buildings  or  other  obstacles,  so  as  te  be 
heard  in  every  direction,  though  often  with  a  consid- 
erable diminution  of  intensity,  as  when  a  carriage  turns 
the  corner  of  a  street. 

The  velocity  of  sound  in  passing  through  solids  is  in 
proportion  to  their  hardness,  and  is  much  greater  than 
in  air  or  water.  A  sound  which  takes  some  time  in  trav- 
eling through  the  air  passes  almost  instantaneously  along 
a  wire  six  hundred  feet  long;  consequently  it  is  heard 
twice — first  as  communicated  by  the  wire  and  after- 
ward through  the  medium  of  the  air.  The  facility 
with  which  the  vibrations  of  sound  are  transmitted  along 
the  grain  of  a  log  of  wood  is  well  known.  Indeed  they 
pass  through  iron,  glass,  and  some  kinds  of  wood,  at  the 
rate  of  18,530  feet  in  a  second.  The  velocity  of  sound 
is  obstructed  by  a  variety  of  circumstances,  such  as  fall- 
ing snow,  fog,  rain,  or  any  other  cause  which  disturbs 
the  homogeneity  of  the  medium  through  which  it  has 
to  pass.  M.  de  Humboldt  says  that  it  is  on  account  of 
the  greater  homogeneity  of  the  atmosphere  during  the 
night  that  sounds  are  then  better  heard  than  during  the 
day,  when  its  density  is  perpetually  changing  from  par- 
tial variations  of  temperature.  His  attention  was  called 
to  this  subject  on  the  plain  surrounding  the  Mission  of 
the  Apures  by  the  rushing  noise  of  the  great  cataracts 
9 


130  TRANSMISSION  OF  SOUND.  SECT.  XVI. 

of  the  Oronoco,  which  seemed  to  be  three  times  as  loud 
by  night  as  by  day.  This  he  illustrated  by  experiment. 
A  tall  glass  half  full  of  champaigne  cannot  be  made  to 
ring  as  long  as  the  effervescence  lasts.  In  order  to  pro- 
duce a  musical  note  the  glass  together  with  the  liquid  it 
contains  must  vibrate  in  unison  as  a  system,  which  it 
cannot  do  in  consequence  of  the  fixed  air  rising  through 
the  wine  and  disturbing  its  homogeneity,  because  the 
vibrations  of  the  gas  being  much  slower  than  those  of 
the  liquid  the  velocity  of  the  sound  is  perpetually  inter- 
rupted. For  the  same  reason  the  transmission  of  sound 
as  well  as  light  is  impeded  in  passing  through  an  atmos- 
phere of  variable  density.  Sir  John  Herschel,  in  his 
admirable  Treatise  on  Sound,  thus  explains  the  phe- 
nomenon: — "It  is  obvious,"  he  says,  "that  sound  as 
well  as  light  must  be  obstructed,  stifled,  and  dissipated 
from  its  original  direction  by  the  mixture  of  air  of  differ- 
ent temperatures,  and  consequently  elasticities;  and 
thus  the  same  cause  which  produces  that  extreme 
transparency  of  the  air  at  night,  which  astronomers 
alone  fully  appreciate,  renders  it  also  more  favorable  to 
sound.  There  is  no  doubt,  however,  that  the  universal 
and  dead  silence,  generally  prevalent  at  night,  renders 
our  auditory  nerves  sensible  to  impressions  which  would 
otherwise  escape  notice.  The  analogy  between  sound 
and  light  is  perfect  in  this  as  in  so  many  other  respects. 
In  the  general  light  of  day  the  stars  disappear.  In  the 
continual  hum  of  voices,  which  is  always  going  on  by 
day,  and  which  reach  us  from  all  quarters  and  never 
leave  the  ear  time  to  attain  complete  tranquillity,  those 
feeble  sounds  which  catch  our  attention  at  night  make 
no  impression.  The  ear,  like  the  eye,  requires  long 
and  perfect  repose  to  attain  its  utmost  sensibility." 

Many  instances  maybe  brought  in  proof  of  the  strength 
and  clearness  with  which  sound  passes  over  the  surface 
of  water  or  ice.  Lieutenant  Foster  was  able  to  carry 
on  a  conversation  across  Fort  Bowen  harbor,  when  fro- 
zen, a  distance  of  a  mile  and  a  half. 

The  intensity  of  sound  depends  upon  the  extent  of 
the  excursions  of  the  fluid  molecules,  on  the  energy  of 
the  transient  condensations  and  dilatations,  and  on  the 
greater  or  less  number  of  particles  which  experience 


SMCT.  XVI.  INTENSITY  OF  SOUND.  ]31 

these  effects.  We  estimate  that  intensity  by  the  im- 
petus of  these  fluid  molecules  on  our  organs,  which  is 
consequently  as  the  square  of  the  velocity,  and  not  by 
their  inertia,  which  is  as  the  simple  velocity.  Were 
the  latter  the  case  there  would  be  no  sound,  because  the 
inertia  of  the  receding  waves  of  air  would  destroy  .the 
equal  and  opposite  inertia  of  those  advancing ;  whence 
it  may  be  concluded  that  the  intensity  of  sound  dimin- 
ishes inversely  as  the  square  of  the  distance  from  its 
origin.  In  a  tube,  however,  the  force  of  sound  does 
not  decay  as  in  open  air,  unless  perhaps  by  friction 
against  the  sides.  M.  Biot  found  from  a  number  of 
highly  interesting  experiments  made  on  the  pipes  of  the 
aqueducts  in  Paris,  that  a  continual  conversation  could 
be  carried  on  in  the  lowest  possible  whisper,  through 
a  cylindrical  tube  about  3120  feet  long,  the  time  of 
transmission  through  that  space  being  2-79  seconds.  In 
most  cases  sound  diverges  in  all  directions  so  as  to  oc- 
cupy at  any  one  time  a  spherical  surface ;  but  Dr.  Young 
has  shown  that  there  are  exceptions,  as  for  example 
when  a  flat  surface  vibrates  only  in  one  direction.  The 
sound  is  then  most  intense  when  the  ear  is  at  right  an- 
gles to  the  surface,  whereas  it  is  scarcely  audible  in  a 
direction  precisely  perpendicular  to  its  edge.  In  this 
case  it  is  impossible  that  the  whole  of  the  surrounding 
air  can  be  affected  in  the  same  manner,  since  the  particles 
behind  the  sounding  surface  must  be  moving  toward  it, 
whenever  the  particles  Before  it  are  retreating.  Hence 
in  one  half  of  the  surrounding  sphere  of  air  its  motions 
are  retrogade,  while  in  the  other  half  they  are  direct ; 
consequently  at  the  edges  where  these  two  portions 
meet,  the  motions  of  the  air  will  neither  be  retrograde 
nor  direct,  and  therefore  it  must  be  at  rest. 

It  appears  from  theory  as  well  as  daily  experience, 
that  sound  is  capable  of  reflection  from  surfaces  (N.  174) 
according  to  the  same  laws  as  light.  Indeed  any  one 
who  has  obs'erved  the  reflection  of  the  waves  from  a 
wall  on  the  side  of  a  river  after  the  passage  of  a  steam- 
boat, will  have  a  perfect  idea  of  the  reflection  of  sound 
and  of  light.  As  every  substance  in  nature  is  more  or 
less  elastic,  it  may  be  agitated  according  to  its  own  law 
by  the  impulse  of  a  mass  of  undulating  air ;  and  recip- 


132  ECHOES.  SECT.  XVI. 

rocally  the  surface  by  its  reaction  will  communicate  its 
undulations  back  again  into  the  air.  Such  reflections 
produce  echoes,  and  as  a  series  of  them  may  take  place 
between  two  or  more  obstacles,  each  will  cause  an  echo 
of  the  original  sound,  growing  fainter  and  fainter  till  it 
dies  away ;  because  sound,  like  light,  is  weakened  by 
reflection.  Should  the  reflecting  surface  be  concave 
toward  a  person,  the  sound  will  converge  toward  him 
with  increased  intensity,  which  will  be  greater  still  if 
the  surface  be  spherical  and  concentric  with  him.  Un- 
dulations of  sound  diverging  from  one  focus  of  an  ellip- 
tical shell  (N.  175)  converge  in  the  other  after  reflec- 
tion. Consequently  a  sound  from  the  one  will  be  heard 
in  the  other  as  if  it  were  close  to  the  ear.  The  rolling 
noise  of  thunder  has  been  attributed  to  reverberation 
between  different  clouds,  which  may  possibly  be  the 
case  to  a  certain  extent.  Sir  John  Herschel  is  of  opin- 
ion, that  an  intensely  prolonged  peal  is  probably  owing 
to  a  combination  of  sounds  because  the  velocity  of  elec- 
tricity being  incomparably  greater  than  that  of  sound, 
the  thunder  may  be  regarded  as  originating  in  every 
point  of  a  flash  of  lightning  at  the  same  instant.  The 
sound  from  the  nearest  point  will  arrive  first,  and  if  the 
flash  run  in  a  direct  line  from  a  person,  the  noise  will 
come  later  and  later  from  the  remote  points  of  its  path 
in  a  continued  roar.  Should  the  direction  of  the  flash 
be  inclined,  the  succession  of  sounds  will  be  more  rapid 
and  intense,  and  if  the  lightning  describe  a  circular  curve 
round  a  person,  the  sound  will  arrive  from  every  point 
at  the  same  instant  with  a  stunning  crash.  In  like 
manner  the  subterranean  noises  heard  during  earth- 
quakes like  distant  thunder,  may  arise  from  the  conse- 
cutive arrival  at  the  ear  of  undulations  propagated  at  the 
same  instant  from  nearer  and  more  remote  points ;  or 
if  they  originate  in  the  same  point,  the  sound  may 
come  by  different  routes  through  strata  of  different  den- 
sities. 

Sounds  under  water  are  heard  very  distinctly  in  the 
air  immediately  above ;  but  the  intensity  decays  with 
great  rapidity  as  the  observer  goes  farther  off,  and  is 
altogether  inaudible  at  the  distance  of  two  or  three 
hundred  yards.  So  that  waves  of  sound,  like  those  of 


-        ••*••• 

SKCT.  XVI.  INTERFERENCE  OF  SOUNDS.  133 

light,  in  passing  from  a  dense  to  a  rare  medium,  are  not 
only  refracted,  but  suffer  total  reflection  at  veiy  oblique 
incidences  (N.  184). 

The  laws  of  interference  extend  also  to  sound.  It  is 
clear  that  two  equal  and  similar  musical  strings  will  be 
in  unison,  if  they  communicate  the  same  number  of 
vibrations  to  the  air  in  the  same  time.  But  if  two  such 
stiings  be  so  nearly  in  unison,  that  one  performs  a  hun- 
dred vibrations  in  a  second,  and  the  other  a  hundred 
and  one  in  the  same  period— during  the  first  few  vibra- 
tions, the  two  resulting  sounds  will  combine  to  form  one 
of  double  the  intensity  of  either,  because  the  aerial  waves 
will  sensibly  coincide  in  time  and  place  ;  but  one  will 
gradually  gain  on  the  other  till  at  the  fiftieth  vibration  it 
will  be  half  an  oscillation  in  advance.  Then  the  waves 
of  air  which  produce  the  sound  being  sensibly  equal,  but 
the  receding  part  of  the  one  coinciding  with  the  advan- 
cing part  of  the  other,  they  will  destroy  one  another  and 
occasion  an  instant  of  silence.  The  sound  will  be  re- 
newed immediately  after,  and  will  gradually  increase 
till  the  hundredth  vibration,  when  the  two  waves  will 
combine  to  produce  a  sound  double  the  intensity  of  either. 
These  intervals  of  silence  and  greatest  intensity,  called 
beats,  will  recur  every  second ;  but  if  the  notes  differ 
much  from  one  another  the  alternations  will  resemble  a 
rattle ;  and  if  the  strings  be  in  perfect  unison  there  will 
be  no  beats,  since  there  will  be  no  interference.  Thus 
by  interference  is  meant  the  coexistence  of  two  undula- 
tions in  which  the  lengths  of  the  waves  are  the  same. 
And  as  the  magnitude  of  an  undulation  may  be  dimin- 
ished by  the  addition  of  another  transmitted  in  the  same 
direction,  it  follows  that  one  undulation  may  be  abso- 
lutely destroyed  by  another  when  waves  of  the  same 
length  are  transmitted  in  the  same  direction,  provided 
that  the  maxima  of  the  undulations  are  equal,  and  that 
one  follows  the  other  by  half  the  length  of  a  wave.  A 
tuning-fork  affords  a  good  example  of  interference. 
When  that  instrument  vibrates,  its  two  branches  alter- 
nately recede  from  and  approach  one  another ;  «ach 
communicates  its  vibrations  to  the  ah*,  and  a  musical 
note  is  the  consequence.  If  the  fork  be  held  upright, 
about  a  foot  from  the  ear,  and  turned  round  its  axis  while 
M 


134  VIBRATION  OF  MUSICAL  STRINGS.    SECT.  XVII. 

vibrating,  at  every  quarter  revolution  the  sound  will 
scarcely  be  heard,  while  at  the  intermediate  points  it 
will  be  strong  and  clear.  This  phenomenon  arises 
from  the  interference  of  the  undulations  of  air  coming 
from  the  two  branches  of  the  fork.  When  the  two 
branches  coincide,  or  when  they  are  at  equal  distances 
from  the  ear,  the  waves  of  air  combine  to  reinforce  each 
other ;  but  at  the  quadrants,  where  the  two  branches 
are  at  unequal  distances  from  the  ear,  the  lengths  of  the 
waves  differ  by  half  an  undulation,  and  consequently 
destroy  one  another. 


SECTION  XVII. 

Vibration  of  Musical  String's— Harmonic  Sounds— Nodes— Vibration  of  Air 
in  Wind  Instruments— Vibration  of  Solids— Vibrating  Plates— Bells- 
Harmony — Sounding  Boards — Forced  Vibrations— Resonance — Speaking 
Machines. 

WHEN  the  particles  of  elastic  bodies  are  suddenly 
disturbed  by  an  impulse,  they  return  to  their  natural 
position  by  a  series  of  isochronous  vibrations,  whose 
rapidity,  force,  and  permanency  depend  upon  the  elas- 
ticity, the  form,  and  the  mode  of  aggregation  which 
unites  the  particles  of  the  body.  These  oscillations  are 
communicated  to  the  air,  and  on  account  of  its  elasticity 
they  excite  alternate  condensations  and  dilatations  in 
the  strata  of  the  fluid  nearest  to  the  vibrating  body  : 
from  thence  they  are  propagated  to  a  distance.  A  string 
or  wire  stretched  between  two  pins,  when  drawn  aside 
and  suddenly  let  go,  will  vibrate  till  its  own  rigidity  and 
the  resistance  of  the  air  reduce  it  to  rest.  These  oscil- 
lations may  be  rotatory  in  every  plane,  or  confined  to  one 
plane,  according  as  the  motion  is  communicated.  In  the 
piano-forte,  where  the  strings  are  struck  by  a  hammer 
at  one  extremity,  the  vibrations  probably  consist  of  a 
bulge  running  to  and  fro  from  end  to  end.  Different 
modes  of  vibration  may  be  obtained  from  the  same  so- 
norous body.  Suppose  a  vibrating  string  to  give  the 
lowest  C  of  the  piano-forte,  which  is  the  fundamental 
note  of  the  string  ;  if  it  be  lightly  touched  exactly  in  the 
middle  so  as  to  retain  that  point  at  rest,  each  half  will 


SKCT.  XVII.     VIBRATION  OP  MUSICAL  STRINGS.  135 

then  vibrate  twice  as  fast  as  the  whole,  but  in  opposite 
directious  ;  the  ventral  or  bulging  segments  will  be  alter- 
nately above  and  below  the  natural  position  of  the  string, 
and  the  resulting  note  will  be  the  octave  above  C.  When 
a  point  at  a  third  of  the  length  of  the  string  is  kept  at 
rest,  the  vibrations  will  be  three  times  as  fast  as  those 
of  the  whole  string,  and  will  give  the  twelfth  above  C. 
When  the  point  of  rest  is  one  fourth  of  the  whole,  the 
oscillations  will  be  four  times  as  fast  as  those  of  the  fun- 
damental note,  and  will  give  the  double  octave  ;  and  so 
on.  These  acute  sounds  are  called  the  harmonics  of 
the  fundamental  note.  It  is  clear  from  what  has  been 
stated,  that  the  string  thus  vibrating  could  not  give  these 
harmonics  spontaneously  unless  it  divided  itself  at  its 
aliquot  parts  into  two,  three,  four,  or  more  segments  in 
opposite  states  of  vibration  separated  by  points  actually 
at  rest.  In  proof  of  this,  pieces  of  paper  placed  on  the 
string  at  the  half,  third,  fouith,  or  other  aliquot  points 
according  to  the  corresponding  harmonic  sound,  will  re- 
main on  it  during  its  vibration,  but  will  instantly  fly  off 
from  any  of  the  intermediate  points.  The  po.ints  of 
rest  called  the  nodal  points  of  the  string,  are  a  mere 
consequence  of  the  law  of  interferences.  For  if  a  rope 
fastened  at  one  end  be  moved  to  and  fro  at  the  other 
extremity  so  as  to  transmit  a  succession  of  equal  waves 
along  it,  they  will  be  successively  reflected  when  they 
arrive  at  the  other  end  of  the  rope  by  the  fixed  point, 
and  in  returning  they  will  occasionally  interfere  with 
the  advancing  waves ;  and  as  these  opposite  undulations 
will  at  certain  points  destroy  one  another,  the  point  of 
the  rope  in  which  this  happens  will  remain  at  rest. 
Thus  a  series  of  nodes  and  ventral  segments  will  be 
produced,  whose  number  will  depend  upon  the  tension 
and  the  frequency  of  the  alternate  motions  communi- 
cated to  the  movable  end.  So  when  a  string  fixed  at 
both  ends  is  put  in  motion  by  a  sudden  blow  at  any^oint 
of  it,  the  primitive  impulse  divides  itself  into  two  pulses 
running  opposite  ways,  which  are  each  totally  reflected 
at  the  extremities,  and  running  back  again  along  the 
whole  length  are  again  reflected  at  the  other  ends.  And 
thus  they  will  continue  to  run  backward  and  forward, 
crossing  one  another  at  each  traverse,  and  occasionally 


136  HARMONIC  SOUNDS.  SECT.  XVII. 

interfering,  so  as  to  produce  nodes ;  so  that  the  motion 
of  a  string  fastened  at  both  ends  consists  of  a  wave  or 
pulse,  continually  doubled  back  on  itself  by  reflection  at 
the  fixed  extremities. 

Harmonics  generally  coexist  with  the  fundamental 
sound  in  the  same  vibrating  body.  If  one  of  the  lowest 
strings  of  the  piano-forte  be  struck,  an  attentive  ear 
will  not  only  hear  the  fundamental  note,  but  will  detect 
all  the  others  sounding  along  with  it,  though  "with  less 
and  less  intensity  as  their  pitch  becomes  higher.  Ac- 
cording to  the  law  of  coexisting  undulations,  the  whole 
string  and  each  of  its  aliquot  parts  are  in  different  and 
independent  states  of  vibration  at  the  same  time ;  and 
as  all  the  resulting  notes  are  heard  simultaneously,  not 
only  the  air  but  the  ear  also  vibrates  in  unison  with 
each  at  the  same  instant  (N.  176). 

Harmony  consists  in  an  agreeable  combination  of 
sounds.  When  two  chords  perform  their  vibrations  in 
the  same  time,  ttjey  are  in  unison.  But  when  their 
vibrations  are  so  related  as  to  have  a  common  period 
after  a  few  oscillations  they  produce  concord.  Thus 
when  the  vibrations  of  two  strings  bear  a  very  simple 
relation  to  each  other,  as  where  one  of  them  makes 
two,  three,  four,  &c.  vibrations  in  the  time  the  other 
makes  one ;  or  if  it  accomplishes  three,  four,  &c.  vibra- 
tions while  the  other  makes  two,  the  result  is  a  concord 
which  is  the  more  perfect  the  shorter  the  common 
period.  In  discords,  on  the  contrary,  the  beats  are 
distinctly  audible,  which  produces  a  disagreeable  and 
harsh  effect,  because  the  vibrations  do  not  bear  a  simple 
relation  to  one  another,  as  where  one  of  two  strings 
makes  eight  vibrations  while  the  other  accomplishes 
fifteen.  The  pleasure  afforded  by  harmony  is  attributed 
by  Dr.  Young  to  the  love  of  order,  and  to  a  predilection 
for  a  regular  repetition  of  sensations  natural  to  the 
human  mind,  which  is  gratified  by  the  perfect  regularity 
and  rapid  recurrence  of  the  vibrations.  The  love  of 
poetry  and  dancing  he  conceives  to  aris,e  in  some  degree 
from  the  rhythm  of  the  one  and  the  regularity  of  the 
motions  in  the  other. 

A  blast  of  air  passing  over  the  open  end  of  a  tube,  as 
over  the  reeds  in  Pan's  pipes ;  over  a  hole  in  one  side, 


SECT.  XVII.    VIBRATION  OF  A  COLUMN  OF  AIR.  137 

as  in  the  flute ;  or  through  the  aperture  called  a  reed 
with  a  flexible  tongue,  as  in  the  clarinet,  puts  the  inter- 
nal column  of  air  into  longitudinal  vibrations  by  the 
alternate  condensations  and  rarefactions  of  its  particles. 
At  the  same  time  the  column  spontaneously  divides 
itself  into  nodes  between  which  the  air  also  vibrates 
longitudinally,  but  with  a  rapidity  inversely  proportional 
to  the  length  of  the  divisions,  giving  the  fundamental 
note  or  one  of  its  harmonics.  The  nodes  are  produced 
on  the  principle  of  interferences  by  the  reflection  of  the 
longitudinal  undulations  of  the  air  at  the  ends  of  the 
pipe,  as  in  the  musical  string,  only  that  in  one  case  the 
undulations  are  longitudinal,  and  in  the  other  transverse. 
A  pipe  either  open  or  shut  at  both  ends  when 
sounded  vibrates  entire,  or  divides  itself  spontaneously 
into  two,  three,  four,  &c.  segments  separated  by  nodes. 
The  whole  column  gives  the  fundamental  note  by 
waves  or  vibrations  of  the  same  length  with  the  pipe. 
The  first  harmonic  is  produced  by  waves  half  as  lon£  as 
the  tube,  the  second  harmonic  by  waves  a  third  as  long, 
and  so  on.  Th^  harmonic  segments  in  an  open  and 
shut  pipe  are  the  same  in  number,  but  differently 
placed.  In  a  shut  pipe  the  two  ends  are  nodes,  but  in 
an  open  pipe  there  is  half  a  segment  at  each  extremity, 
because  the  air  at  these  points  is  neither  rarefied  nor 
condensed,  being  in  contact  with  that  which  is  external. 
If  one  of  the  ends  of  the  open  pipe  be  closed,  its  funda- 
mental note  will  be  an  octave  lower,  the  air  will  now 
divide  itself  into  three,  five,  seven,  &c.  segments ;  and 
the  wave  producing  its  fundamental  note  will  be  twice 
as  long  as  the  pipe,  so  that  it  will  be  doubled  back 
(X.  177).  All  these  notes  may  be  produced  separately, 
by  varying  the  intensity  of  the  blast.  Blowing  steadily 
and  gently,  the  fundamental  note  will  sound ;  when  the 
force  of  the  blast  is  increased,  the  note  will  all  at  once 
start  up  an  octave  ;  when  the  intensity  of  the  wind  is 
augmented,  the  twelfth  will  be  heard,  and  by  continuing 
to  increase  the  force  of  the  blast  the  other  harmonics 
may  be  obtained,  but  no  force  of  wind  will  produce  a 
note  intermediate  between  these.  The  harmonics  of  a 
flute  may  be  obtained  in  this  manner,  from  the  lowest 
C  or  D  upward,  without  altering  the  fingering,  merely 
M  2 


138  VIBRATION  OF  SPRINGS  AND  RODS.  SECT.  XVII. 

by  increasing  the  intensity  of  the  blast,  and  altering  the 
form  of  the  lips.  Pipes  of  the  same  dimensions, 
whether  of  lead,  glass,  or  wood,  give  the  same  tone  as  to 
pitch  under  the  same  circumstances,  which  shows  that 
the  air  alone  produces  the  sound. 

Metal  springs  fastened  at  one  end,  when  forcibly 
bent,  endeavor  to  return  to  rest  by  a  series  of  vibrations, 
which  give  very  pleasing  tones,  as  in  musical  boxes. 
Various  musical  instruments  have  recently  been  con- 
structed, consisting  of  metallic  springs  thrown  into  vibra- 
tion by  a  current  of  air.  Among  the  most  perfect  of  these 
are  Mr.  Wheatstone's  Symphonion,  Concertina,  and  JE>o- 
lian  Organ,  instruments  of  different  effects  and  capabilities, 
but  all  possessing  considerable  execution  and  expression. 

The  Syren  is  an  ingenious  instrument,  devised  by  M. 
Cagniard  de  la  Tour,  for  ascertaining  the  number  of 
pulsations  in  a  second  corresponding  to  each  pitch  :  the 
notes  are  produced  by  jets  of  air  passing  through  small 
apertures  arranged  at  regular  distances  in  a  circle  on 
the  side  of  a  box,  before  which  a  disc  Devolves  pierced 
with  the  same  number  of  holes.  During  a  revolution 
of  the  disc  the  currents  are  alternately  intercepted  and 
allowed  to  pass  as  many  times  as  there  are  apertures  ir 
it,  and  a  sound  is  produced  whose  pitch  depends  on  the 
velocity  of  rotation. 

A  glass  or  metallic  rod,  when  struck  at  one  end,  or 
rubbed  in  the  direction  of  its  length  with  a  wet  finger, 
vibrates  longitudinally  like  a  column  of  air,  by  the  alter- 
nate condensation  and  expansion  of  its  constituent  par- 
ticles, producing  a  clear  and  beautiful  musical  note  of 
a  high  pitch,  on  account  of  the  rapidity  with  which 
these  substances  transmit  sound.  Rods,  surfaces,  and, 
in  genera],  all,  undulating  bodies,  resolve  themselves  into 
nodes.  But  in  surfaces,  the  parts  which  remain  at  rest 
during  their  vibrations  are  lines,  which  are  curved  or 
plane  according  to  the  substance,  its  form,  and  the  mode 
of  vibration.  If  a  little  fine  dry  sand  be  strewed  over 
the  surface  of  a  plate  of  glass  or  metal,  and  if  undula- 
tions be  excited  by  drawing  the  bow  of  a  violin  across 
its  edge,  it  will  emit  a  musical  sound,  and  the  sand 
will  immediately  arrange  itself  in  the  nodal  lines,  where 
alone  it  will  accumulate  and  remain  at  rest,  because  the 


Seer.  XVII.  VIBRATION  OF  PLATES.  139 

segments  of  the  surface  on  each  side  will  be  in  different 
states  of  vibration,  the  one  being  elevated  while  the 
other  is  depressed ;  and  as  these  two  motions  meet  in 
the  nodal  lines,  they  neutralize  one  another.  These 
lines  vary  in  form  and  position  with  the  part  where  the 
bow  is  drawn  across,  and  the  point  by  which  the  plate 
is  held.  The  motion  of  the  sand  shows  in  what  direc- 
tion the  vibrations  take  place.  If  they  be  perpendicular 
to  the  surface,  the  sand  will  be  violently  tossed  up  and 
down,  till  it  finds  the  points  of  rest.  If  they  be  tan- 
gential, the  sand  will  only  creep  along  the  surface  to 
the  nodal  lines.  Sometimes  the  undulations  are  oblique, 
or  compounded  of  both  the  preceding.  If  a  bow  be 
drawn  across  one  of  the  angles  of  a  square  plate  of  glass 
or  metal  held  firmly  by  the  center,  the  sand  will  ar- 
range itself  in  two  straight  lines  parallel  to  the  sides  of 
the  plate,  and  crossing  in  the  center  so  as  to  divide  it 
into  four  equal  squares,  whose  motions  will  be  contrary 
to  each  other.  Two  of  the  diagonal  squares  will  make 
their  excursions  on  one  side  of  the  plate,  while  the 
other  two  make  their  vibrations  on  the  other  side  of  it. 
This  mode  of  vibration  produces  the  lowest  tone  of  the 
plate  (N.  178).  If  the  plate  be  still  held  by  the  center, 
and  the  bow  applied  to  the  middle  of  one  of  the  sides, 
the  vibrations  will  be  more  rapid,  and  the  tone  will  be  a 
fifth  higher  than  in  the  preceding  case ;  now  the  sand 
will  arrange  itself  from  corner  to  corner,  and  will  divide 
the  plate  into  four  equal  triangles,  each  pair  of  which 
will  make  their  excursions  on  opposite  sides  of  the 
plate.  The  nodal  lines  and  pitch  vary  not  only  with 
the  point  where  the  bow  is  applied,  but  with  the  point 
by  which  the  plate  is  held,  which  being  at  rest,  neces- 
sarily determines  the  direction  of  one  of  the  quiescent 
lines.  The  forms  assumed  by  the  sand  in  square 
plates  are  very  numerous,  corresponding  to  all  the  va- 
rious modes  of  vibration.  The  lines  in  circular  plates 
are  even  more  remarkable  for  their  symmetry,  and 
upon  them  the  forms  assumed  by  the  sand  may  be 
classed  in  three  systems.  The  first  is  the  diametrical 
system,  in  which  the  figures  consist  of  diameters  divid- 
ing the  circumference  of  the  plate  into  equal  parts, 
ench  of  which  is  in  a  different  state  of  vibration  from 


140  VIBRATION  OF  PLATES.  SECT.  XVII. 

those  adjacent.  Two  diameters,  for  example,  crossing 
at  right  angles,  divide  the  circumference  into  four  equal 
parts ;  three  diameters  divide  it  into  six  equal  parts ; 
four  divide  it  into  eight,  and  so  on.  In  a  metallic  plate, 
these  divisions  may  amount  to  thirty-six  or  forty.  The 
next  is  the  concentric  system,  where  the  sand  arranges 
itself  in  circles,  having  the  same  center  with  the  plate  ; 
and  the  third  is  the  compound  system,  where  the  figures 
assumed  by  the  sand  are  compounded  of  the  other  two, 
producing  veiy  complicated  and  beautiful  forms.  Ga- 
lileo seems  to  have  been  the  first  to  notice  the  points  of 
rest  and  motion  in  the  sounding-board  of  a  musical 
instrument ;  but  to  Chladni  is  due  the  whole  discovery 
of  the  symmetrical  forms  of  the  nodal  lines  in  vibrating 
plates  (N.  179).  Professor  Wheatstone  has  shown  in 
a  paper  read  before  the  Royal  Society,  in  1833,  that  all 
Chladni' s  figures,  and  indeed  all  the  nodal  figures  of 
vibrating  surfaces,  result  from  very  simple  modes  of 
vibration,  oscillating  isochronously,  and  superposed  upon 
each  other ;  the  resulting  figure  varying  with  the  com- 
ponent modes  of  vibration,  the  number  of  the  super- 
positions, and  the  angles  at  which  they  are  superposed. 
For  example,  if  a  square  plate  be  vibrating  so  as  to  make 
the  sand  arrange  itself  in  straight  lines  parallel  to  one 
side  of  the  plate,  and  if,  in  addition  to  this,  such  vibra- 
tions be  excited  as  would  have  caused  the  sand  to  form 
in  lines  perpendicular  to  the  first  had  the  plate  been 
at  rest,  the  combined  vibrations  will  make  the  sand  form 
in  lines  from  corner  to  corner  (N.  180). 

M.  Savait's  experiments  on  the  vibrations  of  flat  glass 
rulers  are  highly  interesting.  Let  a  lamina  of  glass 
27in-56  long,  0-59  of  an  inch  broad,  0-06  of  an  inch  in 
thickness,  be  held  by  the  edges  in  the  middle,  with  its 
flat  surface  horizontal.  If  this  surface  be  strewed  with 
sand,  and  set  in  longitudinal  vibration  by  rubbing  its 
under  surface  with  a  wet  cloth,  the  sand  on  the  upper 
surface  will  arrange  itself  in  lines  parallel  to  the  ends  of 
the  lamina,  always  in  one  or  other  of  two  systems 
(N.  181).  Although  the  same  one  of  the  two  systems 
will  always  be  produced  by  the  same  plate  of  glass,  yet 
among  different  plates  of  the  preceding  dimensions,  even 
though  cut  from  the  same  sheet  side  by  side*  one  will 


SJCCT.  XVII.  VIBRATION  OP  LAMINJE.  14J 

invariably  exhibit  one  system,  and  the  other  the  other, 
without  any  visible  reason  for  the  difference.  Now  if 
the  positions  of  these  quiescent  lines  be  marked  on  the 
upper  surface,  and  if  the  plate  be  turned  so  that  the 
lower  surface  becomes  the  upper  one,  the  sand  being 
strewed,  and  vibrations  excited  33  before,  the  nodal  lines 
will  still  be  parallel  to  the  ends  of  the  lamina,  but  their 
positions  will  be  intermediate  between  those  of  the 
upper  surface  (N.  182).  Thus  it  appears  that  all  the 
motions  of  one  half  of  the  thickness  of  the  lamina,  or 
ruler,  are  exactly  contrary  to  those  of  the  corresponding 
points  of  the  other  half.  If  the  thickness  of  the  lamina 
be  increased,  the  other  dimensions  remaining  the  same, 
the  sound  will  not  vary,  but  the  number  of  nodal  lines 
will  be  less.  When  the  breadth  of  the  lamina  exceeds 
the  0-6  of  an  inch,  the  nodal  lines-become  curved  and  are 
different  on  the  two  surfaces.  A  great  variety  of  forms 
are  produced  by  increasing  the  breadth  and  changing 
the  form  of  the  surface ;  but  in  all,  it  appears  that  the 
motions  in  one  half  of  the  thickness  are  opposed  to  those 
in  the  other  half. 

M.  Savart  also  found,  by  placing  small  paper  rings 
round  a  cylindrical  tube  or  rod,  so  as  to  rest  upon  it  at 
one  point  only,  that  when  the  tube  or  rod  is  continually 
turned  on  its  axis  in  the  same  direction,  the  rings  slide 
along  during  the  vibrations,  till  they  come  to  a  quiescent 
point,  where  they  rest.  By  tracing  these  nodal  lines  he 
discovered  that  they  twist  in  a  spiral  or  corkscrew  round 
rods  and  cylinders,  making  one  or  more  turns  according 
to  the  length ;  but  at  certain  points,  varying  in  number 
according  to  the  mode  of  vibration  of  the  rod,  the  screw 
stops,  and  recommences  on  the  other  side,  though  it  is 
turned  in  a  contraiy  direction ;  that  is,  on  one  side  it  is 
a  right-handed  screw,  on  the  other  a  left  (N.  183).  The 
nodal  lines  in  the  interior  surface  of  the  tubes  are  per- 
fectly similar  to  those  in  the  exterior,  but  they  occupy 
intermediate  positions.  If  a  small  ivory  ball  be  put 
within  the  tube,  it  will  follow  these  nodal  lines  when 
the  tube  is  made  to  revolve  on  its  axis. 

AH  solids  which  ring  when  struck,  such  as  bells, 
drinking  glasses,  gongs,  &c.,  have  their  shape  momen- 
tarily and  forcibly  changed  by  the  blow,  and  from  their 


142  SYMPATHETIC  VIBRATION.  SECT.  XVII 

elasticity,  or  tendency  to  resume  their  natural  form,  a 
series  of  undulations  takes  place,  owing  to  the  alternate 
condensations  and  rarefactions  _of  the  particles  of  solid 
matter.  These  have  also  their  harmonic  tones,  and 
consequently  nodes.  Indeed  generally,  when  a  rigid 
system  of  any  form  whatever  vibrates  either  transverse- 
ly or  longitudinally,  it  divides  itself  into  a  certain  number 
of  parts,  which  perform  their  vibrations  without  disturb- 
ing one  another.  These  parts  are  at  eveiy  instant  in 
alternate  states  of  undulation  ;  and  as  the  points  or  lines 
where  they  join  partake  of  both  they  remain  at  rest, 
because  the  opposing  motions  destroy  one  another. 

The  air,  notwithstanding  its  rarity,  is  capable  of  trans- 
mitting its  undulations  when  in  contact  with  a  body  sus- 
ceptible of  admitting  and  exciting  them.  It  is  thus  that 
sympathetic  undulations  are  excited  by  a  body  vibrating 
near  insulated  tended  strings,  capable  of  following  its 
undulations,  either  by  vibrating  entire,  or  by  separating 
themselves  into  their  harmonic  divisions.  If  two  chords 
equally  stretched,  of  which  one  is  twice  or  three  times 
longer  than  the  other,  be  placed  side  by  side,  and  if  the 
shorter  be  sounded,  its  vibrations  will  be  communicated 
by  the  air  to  the  other,  which  will  be  thrown  into  such 
a  state  of  vibration  that  it  will  be  spontaneously  divided 
into  segments  equal  in  length  to  the  shorter  string. 
When  a  tuning-fork  receives  a  blow  and  is  made  to  rest 
upon  a  piano-forte  during  its  vibration,  every  string 
which,  either  by  its  natural  length  or  by  its  spontaneous 
subdivisions,  is  capable  of  executing  corresponding  vibra- 
tions, responds  in  a  sympathetic  note.  Some  one  or 
other  of  the  notes  of  an  organ  are  generally  in  unison 
with  one  of  the  panes  or  with  the  whole  sash  of  a  win- 
dow, which  consequently  resounds  when  these  notes 
are  sounded.  A  peal  of  thunder  has  frequently  the 
same  effect.  The  sound  of  very  large  organ-pipes  is 
generally  inaudible  till  the  air  be  set  in  motion  by  the 
undulations  of  some  of  the  superior  accords,  and  then 
its  sound  becomes  extremely  energetic.  Recurring  vi- 
brations occasionally  influence  each  other's  periods.  For 
example,  two  adjacent  organ-pipes  nearly  in  unison,  may 
force  themselves  into  concord ;  and  two  clocks  whose 
rates  differed  considerably  when  separate,  have  been 


S*cr.  XVII.     VIBRATION  OF  PAPER  AND  VELLUM.  143 

known  to  beat  together  when  fixed  to  the  same  wall, 
and  one  clock  has  forced  the  pendulum  of  another  into 
motion,  when  merely  standing  on  the  same  stone  pave- 
ment. These  forced,  oscillations,  which  correspond  in 
their  periods  with  those  of  the  exciting  cause,  are  to  be 
traced  in  every  department  of  physical  science.  Several 
instances  of  them  have  already  occurred  in  this  work. 
Such  are  the  tides,  which  follow  the  sun  and  moon  in  all 
their  motions  and,periods.  The  nutation  of  the  earth's 
axis  also,  which  corresponds  with  the  period,  and  repre- 
sents the  motion  of  the  nodes  of  the  moon,  is  again 
reflected  back  to  the  moon,  and  may  be  traced  in  the 
nutation  of  the1  lunar  orbit.  And  lastly,  the  acceleration 
of  the  moon's  mean  motion  represents  the  action  of  the 
planets  on  the  earth  reflected  by  the  sun  to  the  moon. 

In  consequence  of  the  facility  with  which  the  air 
communicates  undulations,  all  the  phenomena  of  vibrat- 
ing plates  may  be  exhibited  by  sand  strewed  on  paper  or 
parchment,  stretched  over  a  harmonica  glass  or  large 
bell-shaped  tumbler.  In  order  to  give  due  tension  to 
the  paper  or  vellum,  it  must  be  wetted,  stretched  over 
the  glass,  gummed  round  the  edges,  allowed  to  dry,  and 
varnished  over  to  prevent  changes  in  its  tension  from  the 
humidity  of  the  atmosphere.  If  a  circular  disc  of  glass 
be  held  concentrically  over  this  apparatus,  with  its  plane 
parallel  to  the  surface  of  the  paper,  and  set  in  vibration 
by  drawing  a  bow  across  its  edge,  so  as  to  make  sand  on 
its  surface  take  any  of  Chladni's  figures,  the  sand  on  the 
paper  will  assume  the  very  same  form,  in  consequence 
of  the  vibrations  of  the  disc  being  communicated  to  the 
paper  by  the  air.  When  the  disc  is  removed  slowly  in 
a  horizontal  direction,  the  forms  on  the  paper  will  cor- 
respond with  those  on  the  disc,  till  the  distance  is  too 
great  for  the  air  to  convey  the  vibrations.  If  the  disc 
while  vibrating  be  gradually  more  and  more  inclined  to 
the  horizon,  the  figures  on  the  paper  will  vary  by  de- 
grees; and  when  the  vibrating  disc  is  perpendicular  to 
the  horizon,  the  sand  on  the  paper  will  form  into  straight 
lines  parallel  to  the  surface  oT  the  disc,  by  creeping  along  it 
instead  of  dancing  up  and  down.  If  the  disc  be  made  to 
turn  round  its  vertical  diameter  while  vibrating,  the  nodal 
lines  on  the  paper  will  revolve,  and  exactly  follow  the 


144  NODAL  LINES  IN  AtR.  SECT.  XVII. 

motion  of  the  disc.  It  appears  from  this  experiment, 
that  the  motions  of  the  aerial  molecules  in  every  part  of 
a  spherical  wave,  propagated  from  a  vibrating  body  as  a 
center,  are  parallel  to  each  other,  and  not  divergent  like 
the  radii  of  a  circle.  When  a  slow  air  is  played  on  a 
flute  near  this  apparatus,  each  note  calls  up  a  particular 
form  in  the  sand,  which  the  next  note  effaces  to  estab- 
lish its  own.  The  motion  of  the  sand  will  even  detect 
Bounds  that  are  inaudible.  By  the  vibrations  of  sand  on 
a  drum-head  the  besieged  have  discovered  the  direction 
in  which  a  counter-mine  was  working.  M.  Savart,  who 
made  these  beautiful  experiments,  employed  this  appa- 
ratus to  discover  nodal  lines  in  masses  of  air.  He  found 
that  the  air  of  a  room,  when  thrown  into  undulations  by 
the  continued  sound  of  an  organ-pipe,  or  by  any  other 
means,  divides  itself  into  masses  separated  by  nodal 
curves  of  double  curvature,  such  as  spirals,  on  each  side 
of  which  the  air  is  in  opposite  states  of  vibration.  He 
even  traced  these  quiescent  lines  going  out  at  an  open 
window,  and  for  a  considerable  distance  in  the  open  air. 
The  sand  is  violently  agitated  where  the  undulations  of 
the  air  are  greatest,  and  remains  at  rest  in  the  nodal 
lines.  M.  Savart  observed,  that  when  he  moved  his 
head  away  from  a  quiescent  line  toward  the  right  the 
sound  appeared  to  come  from  the  right,  and  when  he 
moved  it  toward  the  left  the  sound  seemed  to  come  from 
the  left,  because  the  molecules  of  air  are  in  different 
states  of  motion  on  each  side  of  the  quiescent  line. 

A  musical  string  gives  a  very  feeble  sound  when  vi- 
brating alone,  on  account  of  the  small  quantity  of  air  set 
in  motion.  But  when  attached  to  a  sounding-board,  as 
in  the  harp  and  piano-forte,  it  communicates  its  undula- 
tions to  that  surface,  and  from  thence  to  every  part  of 
the  instrument ;  so  that  the  whole  system  vibrates  iso- 
chronously,  and  by  exposing  an  extensive  undulating  sur- 
face, which  transmits  its  undulations  to  a  great  mass  of 
air,  the  sound  is  much  reinforced.  The  intensity  is 
greatest  when  the  vibrations  of  the  string  or  sounding 
body  are  perpendicular  to  the  sounding-board,  and  least 
when  they  are  in  the  same  plane  with  it.  The  sound- 
ing-board of  the  piano-forte  is  better  disposed  than  that 
of  any  other  stringed  instrument,  because  the  hammers 


SECT.  XVII.  RESONANCE.  145 

strike  the  strings  so  as  to  make  them  vibrate  at  right 
angles  to  it.  In  the  guitar,  on  the  contrary,  they  are 
struck  obliquely,  which  renders  the  tone  feeble,  unless 
when  the  sides,  which  also  act  as  a  sounding-board,  are 
deep.  It  is  evident  that  the  sounding-board  and  the 
whole  instrument  are  agitated  at  once  by  all  the  super- 
posed vibrations  excited  by  the  simultaneous  or  consecu- 
tive notes  that  are  sounded,  each  having  its  perfect  effect 
independently  of  the  rest..  A  sounding-board  not  only 
reciprocates  the  different  degrees  of  pitch,  but  all  the 
nameless  qualities  of  tone.  This  has  been  beautifully 
illustrated  by  Professor  Wheatstone  in  a  series  of  exper- 
iments on  the  transmission  through  solid  conductors  of 
musical  performances,  from  the  harp,  piano,  violin,  clar- 
inet, &c.  He  found  that  all  the  varieties  of  pitch,  qual- 
ity, and  intensity,  are  perfectly  transmitted  with  their 
relative  gradations,  and  may  be  communicated  through 
conducting  wires  or  rods  of  very  considerable  length,  to 
a  properly  disposed  sounding-board  in  a  distant  apart- 
ment. The  sounds  of  an  entire  orchestra  may  be  trans- 
mitted and  reciprocated  by  connecting  one  end  of  a 
metallic  rod  with  a  sounding-board  near  tbe  orchestra, 
so  placed  as  to  resound  to  all  the  instruments,  and  the 
other  end  with  the  sounding-board  of  a  harp,  piano,  or 
guitar,  in  a  remote  apartment.  Professor  Wheatstone 
observes,  "The  effect  of  this  experiment  is  very  pleas- 
ing; the  sounds,  indeed,  have  so  little  intensity  as  scarcely 
to  be  heard  at  a  distance  from  the  reciprocating  instru- 
ment ;  but  on  placing  the  ear  close  to  it,  a  diminutive 
band  is  heard,  in  which  all  the  instruments  preserve 
their  distinctive  qualities,  and  the  pianos  and  fortes,  the 
crescendos  and  diminuendos,  their  relative  contrasts. 
Compared  with  an  ordinary  band  heard  at  a  distance 
through  the  air,  the  effect  is  as  a  landscape  seen  in  min- 
iature beauty  through  a  concave  lens,  compared  with 
the  same  scene  viewed  by  ordinary  vision  through  a 
murky  atmosphere." 

Every  one  is  aware  of  the  reinforcement  of  sound  by 
the  resonance  of  cavities.  When  singing  or  speaking 
near  the  aperture  of  a  wide-mouthed  vessel,  the  inten- 
sity of  some  one  note  in  unison  with  the  air  in  the  cav- 
ity, is  often  augmented  to  a  great  degree.  A.ny  vessel 
10  N 


146  RESONANCE.  SECT.  XVII. 

will  resound  if  a  body  vibrating  the  natural  note  of  the 
cavity  be  placed  opposite  to  its  orifice,  and  be  large 
enough  to  cover  it ;  or  at  least  to  set  a  large  portion  of 
the  adjacent  air  in  motion.  For  the  sound  will  be  alter- 
nately reflected  by  the  bottom  of  the  cavity  and  the  un- 
dulating body  at  its  mouth.  The  first  impulse  of  the 
undulating  substance  will  be  reflected  by  the  bottom  of 
the  cavity,  and  then  by  the  undulating  body,  in  time  to 
combine  with  the  second  new  impulse.  This  reinforced 
sound  will  also  be  twice  reflected  in  time  to  conspire 
with  the  third  new  impulse  ;  and  as  the  same  process 
will  be  repeated  on  every  new  impulse,  each  will  com- 
bine with  all  its  echoes  to  reinforce  the  sound  pro- 
digiously. Professor  Wheatstone,  to  whose  ingenuity 
we  are  indebted  for  so  much  new  and  valuable  informa- 
tion on  the  theory  of  sound,  has  given  some  veiy  striking 
instances  of  resonance.  If  one  of  the  branches  of  a  vi- 
brating tuning-fork  be  brought  near  the  embouchure  of 
a,  flute,  the  lateral  apertures  of  which  are  stopped  so  as 
to  render  it  capable  of  producing  the  same  sound  as  the 
fork,  the  feeble  and  scarcely  audible  sound  of  the  fork 
will  be  augmented  by  the  rich  resonance  of  the  column 
of  air  within  the  flute,  and  the  tone  will  be  full  and  clear. 
The  sound  will  be  found  greatly  to  decrease  by  closing 
or  opening  another  aperture  ;  for  the  alteration  in  the 
length  of  the  column  of  air  renders  it  no  longer  fit  per- 
fectly to  reciprocate  the  sound  of  the  fork.  This  exper- 
iment may  be  made  on  a  concert  flute  with  a  C  tuning- 
fork.  But  Professor  Wheatstone  observes,  that  in  this 
case  it  is  generally  necessary  to  finger  the  flute  for  B, 
because  when  blown  into  with  the  mouth  the  under-lip 
partly  covers  the  embouchure,  which  renders  the  sound 
about  a  semitone  flatter  than  it  would  be  were  the  em- 
bouchure entirely  uncovered.  He  has  also  shown,  by 
the  following  experiment,  that  any  one  among  several 
simultaneous  sounds  may  be  rendered  separately  audible. 
If  two  bottles  be  selected,  and  tuned  by  filling  them  with 
such  a  quantity  of  water  as  will  render  them  unisonant 
with  two  tuning-forks  which  differ  in  pitch,  on  bringing 
both  of  the  vibrating  tuning-forks  to  the  mouth  of  each 
bottle  alternately,  in  each  case  that  sound  only  will  be 
heard  which  is  reciprocated  by  'the  unisonant  bottle. 


SICT.  XVIII.  A  SPEAKING  MACHINE.  147 

Several  attempts  have  been  made  to  imitate  the  artic- 
ulation of  the  letters  of  the  alphabet.  About  the  year 
1779,  MM.  Kratzenstein  of  St.  Petersburgh,  and  Kem- 
pelen  of  Vienna,  constructed  instruments  which  articu- 
lated many  letters,  words,  and  even  sentences.  Mr. 
Willis  of  Cambridge  has  recently  adapted  cylindrical 
tubes  to  a  reed,  whose  length  can  be  varied  at  pleasure 
by  sliding  joints.  Upon  drawing  out  a  tube  while  a  col- 
umn of  air  from  the  bellows  of  ah  organ  is  passing 
through  it,  the  vowels  are  pronounced  in  the  order,  2,  6, 
a,  o,  u.  On  extending  the  tube  they  are  repeated  after 
a  certain  interval,  in  the  inverted  order,  u,  oy  a,  c,  i.  Af- 
ter another  interval  they  are  flgain  obtained  in  the  direct 
order,  and  so  on.  When  the  pitch  of  the  reed  is  very 
high,  it  is  impossible  to  sound  some  of  the  vowels,  which 
is  in  perfect  correspondence  with  the  human  voice,  fe- 
male singers  being  unable  to  pronounce  u  and  o  in  their 
high  notes.  From  the  singular  discoveries  of  M.  Savart 
on  the  nature  of  the  human  voice,  and  the  investiga- 
tions of  Mr.  Willis  on  the  mechanism  of  the  larynx, 
it  may  be  presumed  that  ultimately  the  utterance-  or 
pronunciation  of  mod ern*langu ages  will  be  conveyed, 
not  only  to  the  eye  but  also  to  the  ear  of  posterity. 
Had  the  ancients  possessed  the  means  of  transmitting 
such  definite  sounds,  the  civilized  world  would ^till  have 
responded  in  sympathetic  notes  at  the  distance  of  many 
ages. 


SECTION  XVIII. 

Refraction — Astronomical  Refraction  and  its  Laws — Formation  of  Tables  of 
Refraction — Terrestrial  Refraction — Its  Quantity — Instances  of  Extraor- 
dinary Refraction — Reflection — Instances  of  Extraordinary  Reflection — 
Loss  of  Light  by  the  Absorbing  Power  of  the  Atmosphere — Apparent 
Magnitude  of  Sun  and  Moon  in  the  Horizon. 

NOT  only  everything  we  hear  but  all  we  see  is  through 
the  medium  of  the  atmosphere.  Without  some  knowl- 
edge of  its  action  upon  light,  it  would  be  impossible  to 
ascertain  the  position  of  the  heavenly  bodies,  or  even  to 
determine  the  exact  place  of  very  distant  objects  upon 
the  surface  of  the  earth ;  for  in  consequence  of  the  re- 


148  ASTRONOMICAL  REFRACTION.        SECT.  XVIII. 

Tractive  power  of  the  air,  no  distant  object  is  seen  in  its 
true  position. 

All  the  celestial  bodies  appear  to  be  more  elevated 
than  they  really  are  ;  because  the  rays  of  light,  instead 
of  moving  through  the  atmosphere  in  straight  lines,  are 
continually  inflected  toward  the  earth.  Light  passing 
obliquely  out  of  a  rare  into  a  denser  medium,  as  from 
vacuum  into  air,  or  from  air  into  water,  is  bent  or  re- 
fracted from  its  course  toward  a  perpendicular  to  that 
point  of  the  denser  surface  where  the  light  enters  it 
(N.  184).  In  the  same  medium,  the  sine  of  the  angle 
contained  between  the  incident  ray  and  the  perpendic- 
ular is  in  a  constant  ratio  to  the  sine  of  the  angle  con- 
tained by  the  refracted  ray  and  the  same  perpendicu- 
lar ;  but  this  ratio  varies  with  the  refracting  medium. 
The  denser  the  medium  the  more  the  ray  is  bent. 
The  barometer  shows  that  the  density  of  the  atmos- 
phere decreases  as  the  height  above  the  earth  increases. 
Direct  experiments  prove  that  the  refractive  power  of 
the  air  increases  with  its  density.  It  follows  therefore 
that  if  the  temperature  be  uniform,  the  refractive  power 
of  the  air  is  greatest  at  the  earth's  surface  and  dimin- 
ishes upward. 

A  ray  of  light  from  a  celestial  object  falling  obliquely 
on  this  variable  atmosphere,  instead  of  being  refracted 
at  once  from  its  course,  is  gradually  more  and  more  bent 
during  its  passage  through  it  so  as  to  move  in  a  vertical 
curved  line,  in  the  same  manner  as  if  the  atmosphere 
consisted  of  an  infinite  number  of  strata  of  different  den- 
sities. The  object  is  seen  in  the  direction  of  a  tangent 
to  that  part  of  the  curve  which  meets  the  eye,  conse- 
quently the  apparent  altitude  (N.  185)  of  the  heavenly 
bodies  is  always  greater  than  their  true  altitude.  Owing 
to  this  circumstance,  the  stars  are  seen  above  the  hori- 
zon after  they  are  set,  and  the  day  is  lengthened  from 
a  part  of  the  sun  being  visible,  though  he  really  is  behind 
the  rotundity  of  the  earth.  It  would  be  easy  to  de- 
termine the  direction  of  a  ray  of  light  through  the  at- 
mosphere if  the  law  of  the  density  were  known  ;  but  as 
this  law  is  perpetually  varying  with  the  temperature, 
the  case  is  very  complicated.  When  rays  pass  perpen- 
dicularly from  one  medium  into  another,  they  are  not 


SECT.  XVIII.         ASTRONOMICAL  REFRACTION.  149 

bent ;  and  experience  shows,  that  in  the  same  surface, 
though  the  sines  of  the  angles  of  incidence  and  refrac- 
tion retain  the  same  ratio,  the  refraction  increases  with 
the  obliquity  of  incidence  (N.  184).  Hence  it  appears 
that  the  refraction  is  greatest  at  the  horizon,  and  at  the 
zenith  there  is  none.  But  it  is  proved  that  at  all  heights 
above  ten  degrees,  refraction  varies  nearly  as  the  tangent 
of  the  angular  distance  of  the  object  from  the  zenith, 
and  wholly  depends  upon  the  heights  of  the  barometer 
and  thermometer.  For  the  quantity  of  refraction  at  the 
same  distance  from  the  zenith  varies  nearly  as  the  height 
of  the  barometer,  the  temperature  being  constant;  and 
the  effect  of  the  variation  of  temperature  is  to  diminish 
the  quantity  of  refraction  by  about  its  480th  part  for 
every  degree  in  the  rise  of  Fahrenheit's  thermometer. 
Not  much  reliance  can  be  placed  on  celestial  observa- 
tions, within  less  than  ten  or  twelve  degrees  of  the 
horizon,  on  account  of  irregular  variations  in  the  density 
of  the  air  near  the  surface  of  the  earth,  which  are 
sometimes  the  cause  of  very  singular  phenomena.  The 
humidity  of  the  ah'  produces  no  sensible  effect  on  its 
refractive  power. 

Bodies,  whether  luminous  or  not,  are  only  visible  by 
the  rays  which  proceed  from  them.  As  the  rays  must 
pass  through  strata  of  different  densities  in  coming  to  us, 
it  follows  that  with  the  exception  of  stars  in  the  zenith, 
no  object  either  in  or  beyond  our  atmosphere  is  seen  in 
its  true  place.  But  the  deviation  is  so  smalHp  ordinary 
cases  that  it  causes  no  inconvenience,  though  in  astro- 
nomical and  trigonometrical  observations  diie  allowance 
must  be  made  for  the  effects  of  refraction.  Dr.  Brad- 
ley's  tables  of  refraction  were  formed  by  observing  the 
zenith  distances  of  the  sun  at  his  greatest  declinations, 
and  the  zenith  distances  of  the  pole-star  above  and  below 
the  pole.  The  sum  of  these  four  quantities  is  equal  to 
180°,  diminished  by  the  sum  of  the  four  refractions, 
whence  the  sum  of  the  four,  refractions  was  obtained  ; 
and  from  the  law  of  the  variation  of  refraction  determined 
by  theory,  he  assigned  the  quantity  due  to  each  altitude 
(N.  186).  The  mean  horizontal  refraction  is  about 
35'  6",  and  at  the  height  of  forty-five  degrees  it  is  58"-36. 
The  effect  of  refraction  upon  the  same  star  above  and 


150  TERRESTRIAL  REFRACTION.         SECT.  XVIII. 

below  the  pole  was  noticed  by  Alhazen,  a  Saracen 
astronomer  of  Spain,  in' the  ninth  century,  but  its  exis- 
tence, was  known  to  Ptolemy  in  the  second,  though  he 
was  ignorant  of  its  quantity. 

The  refraction  of  a  terrestrial  object  is  estimated  dif- 
ferently from  that  of  a  celestial  body.  It  is  measured 
by  the  angle  contained  between  the  tangent  to  the 
curvilineal  path  of  the  ray  where  it  meets  the  eye,  and 
the  straight  line  joining  the  eye  and  the  object  (N.  187). 
Near  the  earth's  surface  the  path  of  the  ray  may  be 
supposed  to  be  circular ;  and  the  angle  at  the  center  of 
the  earth  corresponding  to  this  path  is  called  the  hori- 
zontal angle.  The  quantity  of  terrestrial  refraction  is 
obtained  by  measuring  contemporaneously  the  elevation 
of  the  top  of  a  mountain  above  a  point  in  the  plain  at  its 
base,  and  the  depression  of  that  point  below  the  top  of 
the  mountain.  The  distance  between  these  two  sta- 
tions is  the  chord  of  the  horizontal  angle  ;  and  it  is  easy 
to  prove  that  double  the  refraction  is  equal  to  the 
horizontal  angle,  increased  by  the  difference  between 
the  apparent  elevation  and  4he  apparent  depression. 
Whence  it  appears  that  in  the  mean  state  of  the  atmos- 
phere, the  refraction  is  about  the  fourteenth  part  of  the 
horizontal  angle. 

Some  very  singular  appearances  occur  from  the  acci- 
dental expansion  or  condensation  of  the  strata  of  the 
atmosphere  contiguous  to  the  surface  of  the  earth,  by 
which  distant  objects,  instead  of  being  elevated,  are  de- 
pressed. Sometimes  being  at  once  both  elevated  and 
depressed  they  appear  double,  one  of  the  images  being 
direct,  and  the  other  inverted..  In  consequence  of  the 
upper  edges  of  the  sun  and  moon  being  less  refracted 
than  the  lower,  they  often  appear  to  be  oval  when  near 
the  horizon.  The  looming  also  or  elevation  of  coasts, 
mountains,  and  ships,  when  viewed  across  the  sea, 
arises  from  unusual  refraction.  A  friend  of  the  au- 
thor, while  standing  on  the  plains  of  Hindostan,  saw 
the  whole  upper  chain  of  the  Himalaya  mountains  start 
into  view,  from  a  sudden  change  in  the  density  of  the 
air,  occasioned  by  a  heavy  shower  after  a  very  long 
course  of  dry  and  hot  weather.  Single  and  double  im- 
ages of  objects  at  sea,  arising  from  sudden  changes  of 


S«cr.  XVm.    PHENOMENA  FROM  REFLECTION.  151 

temperature  which  are  not  so  soon  communicated  to  the 
water  on  account  of  its  density  as  to  the  air,  occur  more 
rarely  and  are  of  shorter  duration  than  similar  appear- 
ances on  land.  In  1818,  Captain  Scoresby,  whose  ob- 
servations on  the  phenomena  of  the  polar  seas  are  so 
valuable,  recognized  his  father's  ship  by  its  inverted 
image  in -the  air,  although  the  vessel  itself  was  below 
the  horizon.  He  afterward  found  that  she  was  seven- 
teen miles  beyond  the  horizon,  and  thirty  miles  distant. 
Two  images  are  sometimes  seen  suspended  in  the  air 
over  a  ship,  one  direct  and  the  other  inverted,  with  their 
topmasts  or  their  hulls  meeting,  according  as  the  in- 
verted image  is  above  or  below  the  direct  image  (N.  188^. 
Dr.  Wollaston  has  proved  that  these  appearances  are 
owing  to  the  refraction  of  the  rays  through  media  of 
different  densities,  by  the  veiy  simple  experiment  of 
looking  along  a  red-hot  poker  at  a  distant  object.  Two 
images  are  seen,  one  direct  and  another  inverted,  in 
consequence  of  the  change  induced  by  the  heat  in  the 
density  of  the  adjacent  air.  He  produced  the  same 
effect  by  a  saline  or  saccharine  solution  with  water  and 
spirit  of  wine  floating  upon  it  (N.  189). 

Many  of  the  phenomena  that  have  been  ascribed  to 
extraordinary  refraction  seem  to  be  occasioned  J>y  a 
partial  or  total  reflection  of  the  rays  of  light  at  the  sur- 
faces of  strata  of  different  densities  (N.  184).  It  is  well 
known  that  when  light  falls  obliquely  uponjhe  external 
surface  of  a  transparent  medium,  as  on  a  plate  »i  glass 
or  stratum  of  air,  one  portion  is  reflected  and  the  other 
transmitted.  But  when  light  falls  very  obliquely  upon 
the  internal  surface,  the  whole  is  reflected  and  not  a 
ray  is  transmitted.  In  all  cases  the  an^es  made  by 
the  incident  and  reflected  rays  with  a  perpendicular  to 
the  surface  being  equal,  as  the  brightness  of  the  re- 
flected image  depends  on  the  quantity  of  light,  those 
arising  from  total  reflection  must  be  by  far  the  most 
vivid.  The  delusive  appearance  of  water,  so  well 
known  to  African  travelers  and  to  the  Arab  of  the  des- 
ert as  the  Lake  of  the  Gazelles,  is  ascribed  to  the  re- 
flection which  takes  place  between  strata  of  air  of  dif- 
ferent densities,  owing  to  radiation  of  heat  from  the 
arid  sandy  plains.  The 'mirage  described  by  Captain 


152  EXTRAORDINARY  REFLECTION.      SECT.  XVIII. 

Mundy  in  his  Journal  of  a  Tour  in  India  probably 
arises  from  this  cause.  A  deep  precipitous  valley  be- 
low us,  at  the  bottom  of  which  I  had  seen  one  or  two 
miserable  villages  in  the  morning,  bore  in  the  evening  a 
complete  resemblance  to  a  beautiful  lake ;  the  vapor 
which  played  the  part  of  water  ascending  nearly  half 
way  up  the  sides  of  the  vale,  and  on  its  bright  surface 
trees  and  rocks  being  distinctly  reflected.  I  had  not 
been  long  contemplating  this  phenomenon,  before  a 
sudden  storm  came  on  and  dropped  a  curtain  of  clouds 
over  the  scene." 

An  occurrence  which  happened  on  the  18th  of  No- 
vember, 1804,  was  probably  produced  by  reflection. 
Dr.  Buchan,  while  watching  the  rising  sun  from  the 
cliff  about  a  mile  to  the  east  of  Brighton,  at  the  instant 
the  solar  disc  emerged  from  the  surface  of  the  ocean, 
saw  the  cliff  on  which  he  was  standing,  a  windmill,  his 
own  figure  and  that  of  a  friend,  depicted  immediately 
opposite  to  him  on  the  sea.  This  appearance  lasted 
about  ten  minutes,  till  the  sun  had  risen  nearly  his  own 
diameter  above  the  surface  of  the  waves.  The  whole 
then  seemed  to  be  elevated  into  the  air  and  successively 
vanished.  The  rays  of  the  sun  fell  upon  the  cliff  at  an 
incidence  of  73°  from  the  perpendicular,  and  the  sea 
was  covered  with  a  dense  fog  many  yards  in  height 
which  gradually  receded  before  the  rising  sun.  When 
extraordinary  refraction  takes  place  laterally,  the  strata 
of  variable  density  are  perpendicular  to  the  horizon, 
and  if  combined  with  vertical  refraction,  the  objects 
are  magnified  as  when  seen  through  a  telescope.  From 
this  cause,,  on  'the  2(>'th  of  July,  1798,  the  cliffs  of 
France,  fifty' "miles  oi'f,  were  seen  as  distinctly  from 
Hastings  as  if  they  had  been  close  at  hand ;  and  even 
Dieppe  was  said  to  have  been  visible  in  the  afternoon. 

The  stratum  of  air  in  the  horizon  is  so  much  thicker 
and  more  dense  than  the  stratum  in  the  vertical,  that 
the  sun's  light  is  diminished  1300  times  in  passing 
through  it,  which  enables  us  to  look  at  him  when  setting 
without  being  dazzled.  The  loss  of  light  and  conse- 
quently of  heat  by  the  absorbing  power  of  the  atmos- 
phere, increases  with  the  obliquity  of  incidence.  Of 
ten  thousand  rays  falling  on  its  surface,  8123  arrive  at  a 


SECT.  XIX.  ATMOSPHERIC  ABSORPTION.  153 

given  point  of  the  earth  if  they  fall  perpendicularly ; 
7024  arrive,  if  the  angle  of  direction  be  fifty  degrees ; 
2831,  if  it  be  seven  degrees ;  and  only  five  rays  will 
arrive  through  a  horizontal  stratum.  Since  so  great  a 
quantity  of  light  is  lost  in  passing  through  the  atmos- 
phere, many  celestial  objects  may  be  altogether  invisible 
from  the  plain,  which  may  be  seen  from  elevated  situ- 
ations. Diminished  splendor,  and  the  false  estimate 
we  make  of  distance  from  the  number  of  intervening 
objects,  lead  us  to  suppose  the  sun  and  moon  to  be 
much  larger  when  in  the  horizon  than  at  any  other  al- 
titude, though  their  apparent  diameters  are  then  some- 
what less.  Instead  of  the  sudden  transitions  of  light 
and  darkness,  the  reflective  power  of  the  air  adorns  na- 
ture with  the  rosy  and  golden  hues  of  the  Aurora  and 
twilight.  Even  when  the  sun  is  eighteen  degrees  be- 
low the  horizon,  a  sufficient  portion  of  light  remains  to 
show,  that  at  the  height  of  thirty  miles  it  is  still  dense 
enough  to  reflect  light.  The  atmosphere  scatters  the 
sun's  rays,  and  gives  all  the  beautiful  tints  and  cheerful- 
ness of  day.  It  transmits  the  blue  light  in  greatest 
abundance ;  the  higher  we  ascend,  the  sky  assumes  a 
deeper  hue ;  but  in  the  expanse  of  space,  the  sun  and 
stars  must  appear  like  brilliant  specks  in  profound 
blackness. 


SECTION  XIX. 

Constitution  of  Light  according  to  Sir  Isaac  Ne^ 
— Colors  of  Bodies— Constitution  of  Light  accord 
ster — New  Colors  in  the  Solar  Spectrum — Frau 
Dispersion  of  Light— The  Achromatic  Telescope— 
Accidental  and  Complementary  Colors— M.  Plateau's 
Theory  of  Accidental  Colors. 

IT  is  impossible  thus  to  trace  the  path  of  a  sunbeam 
through  our  atmosphere  without  feeling  a  desire  to 
know  its  nature,  by  what  power  it  traverses  the  immen- 
sity of  space,  and  the  various  modifications  it  undergoes 
at  the  surfaces  and  in  the  interior  of  terrestrial  sub- 
stances. 

Sir  Isaac  Newton  proved  the  compound  nature  of 
white  light  as  emitted  from  the  sun,  by  passing  a  sun- 
beam through  a  glass  prism  (N.  190),  which  separating 


154  CONSTITUTION  OF  LIGHT.  SECT.  XIX. 

the  rays  by  refraction,  formed  a  spectrum  or  oblong 
image  of  the  sun,  consisting  of  seven  colors,  red,  orange, 
yellow,  green,  blue,  indigo,  and  violet ;  of  which  the 
red  is  the  least  refrangible  and  the  violet  the  most.  But 
when  he  reunited  these  seven  rays  by  means  of  a  lens, 
the  compound  beam  became  pure  white  as  before.  He 
insulated  each  colored  ray ;  and  finding  that  it  was  no 
longer  capable  of  decomposition  by  refraction,  concluded 
that  white  light  consists  of  seven  kinds  of  homogeneous 
light,  and  that  to  the  same  color  the  same  refrangibility 
ever  belongs,  and  to  the  same  refrangibility  the  same 
color.  Since  the  discoveiy  of  absorbent  media,  how- 
ever, it  appears  that  this  is  not  the  constitution  of  the 
solar  spectrum. 

We  know  of  no  substance  that  is  either  perfectly 
opaque  or  perfectly  transparent.  Even  gold  may  be 
beaten  so  thin  as  to  be  pervious  to  light.  On  the  con- 
trary, the  clearest  crystal,  the  purest  air  or  water,  stops 
or  absorbs  its  rays  when  transmitted,  and  gradually  ex- 
tinguishes them  as  they  penetrate  to  greater  depths. 
On  this  account  objects  cannot  be  seen  at  the  bottom  of 
very  deep  water,  and  many  more  stars  are  visible  to  the 
naked  eye  from  the  tops  of  mountains  than  from  the 
valleys.  The  quantity  of  light  that  is  incident  on  any 
transparent  substance  is  always  greater  than  the  sum  of 
the  reflected  and  refracted  rays.  A  small  quantity  is 
irregularhy-efleeted  in  all  directions  by  the  imperfec- 
tions of  the  polish  by  which  we  are  enabled  to  see  the 
surface  ;  but  a  much  greater  portion  is  absorbed  by  the 
body.  Bodies  that  reflect  all  the  rays  appear  white, 
those  that  absorb  them  all  seem  black  ;  but  most  sub- 
stances, after  decomposing  the  white  light  which  falls 
upon  them,  reflect  some  colors  and  absorb  the  rest.  A 
violet  reflects  the  violet  rays  alone,  and  absorbs  the 
others.  Scarlet  cloth  absorbs  almost  all  the  colors  ex- 
cept red.  Yellow  cloth  reflects  the  yellow  rays  most 
abundantly,  and  blue  cloth  those  that  are  blue.  Con- 
sequently color  is  not  a  property  of  matter,  but  arises 
from  the  action  of  matter  upon  light.  Thus  a  white 
riband  reflects  all  the  rays,  but  when  dyed  red  the  par- 
ticles of  the  silk  acquire  the  property  of  reflecting  the 
red  rays  most  abundantly  and  of  absorbing  the  others. 


S*CT.  XIX.  ABSORPTION  OF  LIGHT.  155 

Upon  this  property  of  unequal  absorption,  the  colors  of 
transparent  media  depend.  For  they  also  receive  their 
color  from  their  power  of  stopping  or  absorbing  some  of 
the  colors  of  white  light  and  transmitting  others.  As 
for  example,  black  and  red  inks,  though  equally  homo- 
geneous, absorb  different  kinds  of  rays ;  and  when  ex- 
posed to  the  sun,  they  become  heated  in  different  de- 
grees ;  while  pure  water  seems  to  transmit  all  rays 
equally,  and  is  not  sensibly  heated  by  the  passing  light 
of  the  sun.  The  rich  dark  light  transmitted  by  a  smalt- 
blue  finger-glass  is  not  a  homogeneous  color  like  the 
blue  or  indigo  of  the  spectrum,  but  is  a  mixture  of  all 
the  colors  of  white  light  which  the  glass  has  not  ab- 
sorbed. The  colors  absorbed  are  such  as  mixed  with 
the  blue  tint  would  form  white  light.  When  the  spec- 
trum of  seven  colors  is  viewed  through  a  thin  plate  of 
this  glass  they  are  all  visible ;  and  when  the  plate  is 
very  thick,  every  color  is  absorbed  between  the  extreme 
red  and  the  extreme  violet,  the  interval  being  perfectly 
black  :  but  if  the  spectrum  be  viewed  through  a  certain 
thickness  of  the  glass  intermediate  between  the  two,  it 
will  be  found  that  the  middle  of  the  red  space,  the  whole 
of  the  orange,  a  great  part  of  the  green,  a  considerable 
part  of  the  blue,  a  little  of  the  indigo,  and  a  very  little 
of  the  violet,  vanish,  being  absorbed  by  the  blue  glass  : 
and  that  the  yellow  rays -occupy  a  larger  space,  cover- 
ing part  of  that  formerly  occupied  by  the  orange  on  one 
side,  and  by  the  green  on  the  other.  So  that  the  blue 
glass  absorbs  the  red  light,  which  when  mixed  with  the 
yellow  constitutes  orange  ;  and  also  absorbs  the  blue 
light,  which  when  mixed  with  the  yellow  forms  the 
part  of  the  green  space  next  to  the  yellow.  Hence  by 
absorption,  green  light  is  decomposed  into  yellow  and 
blue,  and  orange  light  into  yellow  and  red.  Conse- 
quently the  orange  and  green  rays,  though  incapable  of 
decomposition  by  refraction,  can  be  resolved  by  absorp- 
tion, and  actually  consist  of  two  different  colors  possess- 
ing the  same'  degree  of  refrangibility.  Difference  of 
color,  therefore,  is  not  a  test  of  difference  of  refrangi- 
bility, and  the  conclusion  deduced  by  Newton  is  no 
longer  admissible  as  a  general  truth.  By  this  analysis 
of  the  spectrum,  not  only  with  blue  glass,  but  with  a 


156  THE  SOLAR  SPECTRUM.  SECT.  XIX. 

variety  of  colored  media,  Sir  David  Brewster,  so  justly 
celebrated  for  his  optical  discoveries,  has  proved  that 
the  solar  spectrum  consists  of  three  primary  colors,  red, 
yellow,  and  blue,  each  of  which  exists  throughout  its 
whole  extent,  but  with  different  degrees  of  intensity  in 
different  parts  ;  and  that  the  superposition  of  these  three 
produces  all  the  seven  hues  according  as  each  primary 
color  is  an  excess  or  defect.  Since  a  certain  portion  of 
red,  yellow,  and  blue  rays  constitute  white  light,  the 
color  of  any  point  of  the  spectrum  may  be  considered 
as  consisting  of  the  predominating  color  at  that  point 
mixed  with  white  light.  Consequently,  by  absorbing 
the  excess  of  any  color  at  any  point  of  the  spectrum 
above  what  is  necessary  to  form  white  light,  such  white 
light  will  appear  at  that  point  as  never  mortal  eye 
looked  upon  before  this  experiment,  since  it  possesses 
the  remarkable  property  of  remaining  the  same  after 
any  number  of  refractions,  and  of  being  capable  of  de- 
composition by  absorption  alone. 

In  addition  to  the  seven  colors  of  the  Newtonian  spec- 
trum, Sir  John  Herschel  has  discovered  a  set  of  very 
dark  red  rays  beyond  the  red  extremity  of  the  spec- 
trum, which  can  only  be  seen  when  the  eye  is  defended 
from  the  glare  of  the  other  colors  by  a  dark  blue  cobalt 
glass.  He  has  also  found  that  beyond  the  extreme 
violet  there  are  visible  rays  of  a  lavender  gray  color, 
which  may  be  seen  by  throwing  the  spectrum  on  a 
sheet  of  paper  moistened  by  the  carbonate  of  soda. 
The  illuminating  power  of  the  different  rays  of  the  spec- 
trum varies  with  the  color.  The  most  intense  light  is 
in  the  mean  yellow  ray. 

When  the  prism  is  very  perfect  and  the  sunbeam 
small,  so  that  the  spectrum  may  be  received  on  a  sheet 
of  white  paper  in  its  utmost  state  of  purity,  it  presents 
the  appearance  of  a  riband  shaded  with  all  the  prismatic 
colors,  having  its  breadth  irregularly  striped  or  subdi- 
vided by  an  indefinite  number  of  dark,  and  sometimes 
black,  lines.  The  greater  number  of  these  rayless  lines 
are  so  extremely  narrow  that  it  is  impossible  to  see 
them  in  ordinary  circumstances.  The  best  method  is 
to  receive  the  spectrum  on  the  object  glass  of  a  tele- 
scope, so  as  to  magnify  them  sufficiently  to  render  them 


SECT.  XIX.  FRAUNHOFER'S  LINES.  157 

visible.  This  experiment  may  also  be  made,  but  in  an 
imperfect  manner,  by  viewing  a  narrow  slit  between  two 
nearly  closed  window-shutters  through  a  very  excellent 
glass  prism  held  close  to  the  eye,  with  its  refracting 
angle  parallel  to  the  line  of  light.  The  rayless  lines  in 
the  red  portion  of  the  spectrum  become  most  visible  as 
the  sun  approaches  the  horizon,  while  those  in  the  blu» 
extremity  are  most  obvious  in  the  middle  of  the  day. 
AVhen  the  spectrum  is  formed  by  the  sun's  rays,  either 
direct  or  indirect — as  from  the  sky,  clouds,  rainbow,  moon, 
or  planets — the  black  bands  are  always  found  to  be  in 
the  same  parts  of  the  spectrum,  and  under  all  circum- 
stances to  maintain  the  same  relative  positions,  breadths, 
and  intensities.  Similar  dark  lines  are  also  seen  in  the 
light  of  the  stars,  in  the  electric  light,  and,  in  the  flame 
of  combustible  substances,  though  differently  arranged, 
each  star  and  each  flame  having  a  system  of  dark  lines 
peculiar  to  itself,  which  remains  the  same  under  every 
circumstance.  Dr.  Wollaston  and  M.  Fraunhofer  of 
Munich  discovered  these  lines  deficient  of  rays  inde- 
pendently of  each  other.  M.  Fraunhofer  found  that 
their  number  extends  to  nearly  six  hundred.  There  are 
bright  lines  in  the  solar  spectrum  which  also  maintain  a 
fixed  position.  Among  the  dark  lines,  M.  Fraunhofer 
selected  seven  of  the  most  remarkable,  and  determined 
their  distances  so  accurately,  that  they  now  form  stand- 
ard and  invariable  points  of  reference  for  measuring  the 
refractive  powers  of  different  media  on  the  rays  of  light, 
which  renders  this  department  of  optics  as  exact  as  any 
of  the  physical  sciences.  These  lines  are  designated 
by  the  letters  of  the  alphabet,  beginning  with  B,  which 
is  in  the  red  near  the  end  of  the  spectrum  ;  c  is  farther 
advanced  in  the  red ;  D  is  in  the  orange ;  E,  in  the 
green  ;  F,  in  the  blue;  G,  in  the  indigo;  and  H,  in  the 
violet.  By  means  of  these  fixed  points,  M.  Fraunhofer 
has  ascertained  from  prismatic  observation  the  refrangi- 
bility  of  seven  of  the  principal  rays  in  each  often  differ- 
ent substances  solid  and  liquid.  The  refraction  increased 
in  all  from  the  red  ta  the  violet  end  of  the  spectrum ; 
but  so  irregularly  for  each  ray  and  in  each  medium,  that 
no  law  (ioukl  be  discovered.  The  rays  that  are  wanting 
in  the  solar  spectrum  which  occasion  the  dark  lines, 
O 


158  DISPERSION  OF  LIGHT.  SECT.  XIX. 

were  supposed  to  be  absorbed  by  the  atmosphere  of  the 
sun.  If  they  were  absorbed  by  the  earth's  atmosphere, 
the  very  same  rays  would  be  wanting  in  the  spectra 
from  the  light  of  the  fixed  stars,  which  is  not  the  case  ; 
for  it  has  already  been  stated  that  the  position  of  the 
dark  lines  is  not  the  same  in  spectra  from  starlight  and 
from  the  light  of  the  sun.  The  solar  rays  reflected 
from  the  moon  and  .planets  would  most  likely  be  mod- 
ified also  by  their  atmospheres,  but  they  are  not :  for 
the  dark  lines  have  precisely  the  same  positions  in  the 
spectra,  from  the  direct  and  reflected  light  of  the  sun. 
But  the  annular  eclipse  which  happened  on  the  15th  of 
May,  1836,  afforded  Professor  Forbes  the  means  of 
proving  that  the  dark  lines  in  question  cannot  be  attrib- 
uted to  the  absorption  of  the  solar  atmosphere ;  they 
were  neither  broader  nor  more  numerous  in  the  spec- 
trum formed  during  that  phenomenon  than  at  any  other 
time,  though  the  rays  came  only  from  the  circumference 
of  the  sun's  disc,  and  consequently  had  to  traverse  a 
greater  depth  of  his  atmosphere.  We  are  therefore 
still  ignorant  of  the  cause  of  these  rayless  bands. 

A  sunbeam  received  on  a  screen,  after  passing  through 
a  small  round  hole  in  a  window-shutter,  appears  like  a 
round  white  spot ;  but  when  a  prism  is  interposed,  the 
beam  no  longer  occupies  the  same  space.  It  is  separa- 
ted into,  the  prismatic  colors,  and  spread  over  a  line  of 
considerable  length,  while  its  breadth  remains  the  same 
with  that  of  the  white  spot.  The  act  of  spreading  or 
separation  is  called  the  dispersion  of  the  colored  rays. 
Dispersion  always  takes  place  in  the  plane  of  refraction, 
and  is  greater  as  the  angle  of  incidence  is  greater.  It 
varies  inversely  as  the  length  of  a  wave  of  light,  and 
directly  as  its  velocity :  hence  toward  the  blue  end  of 
the  spectrum,  where  the  undulations  of  the  rays  are 
least,  the  dispersion  is  greatest.  Substances  have  veiy 
different  dispersive  powers ;  that  is  to  say  the  spectra 
formed  by  two  equal  prisms  of  different  substances  under 
precisely  the  same  circumstances,  are  of  different 
lengths.  Thus,  if  a  prism  of  flint  glass  and  one  of  crown 
glass  of  equal  refracting  angles  be  presented  to  two  rays 
of  white  light  at  equal  angles,  it  will  be  found,  that  the 
space  over  which  the  colored  rays  are  dispersed  by  the 


SJCT.  XIX.         THE  ACHROMATIC  TELESCOPE.  159 

flint  glass  is  much  greater  than  the  space  occupied  by 
that  produced  by  the  crown  glass ;  and  as  the  quantity 
of  dispersion  depends  upon  the  refracting  angle  of  the 
prism,  the  angles  of  the  two  prisms  may  be  made  such, 
that  when  the  prisms  are  placed  close  together  with  tbjeir 
edges  turned  opposite  ways,  they  will  exactly  oppose 
each  other's  action,  and  will  refract  the  colored  rays 
equally  but  in  contrary  directions,  so  that  an  exact  com- 
pensation will  be  effected,  and  the  light  will  be  refracted 
without  color  (N.  191).  The  achromatic  telescope  is 
constructed  on  this  principle.  It  consists  of  a  tube  with 
an  object  glass  or  lens  at  one  end  to  bring  the  rays  to  a 
focus  and  form  an  image  of  the  distant  object,  and  a 
magnifying  glass  at  the  other  end  to  view  the  knage 
thus  formed.  Now  it  is  found  that  the  object-glass, 
instead  of  making  the  rays  converge  to  one  point,  dis- 
perses them,  and  gives  a  confused  and  colored  image : 
but  by  constructing  it  of  two  lenses  in  contact,  one  of 
flint  and  the  other  of  crown  glass  of  certain  forms  and 
proportions,  the  dispersion  is  counteracted,  and  a  per- 
fectly well  defined  and  colorless  image  of  the  object  is 
formed  (N.  192).  It  was  thought  to  be  impossible  to 
produce  refraction  without  color,  till  Mr.  Hall,  a  gentle- 
man of  "Worcestershire,  constructed  a  telescope  on  this 
principle  in  the  year  1733  ;  and  twenty-five  years  after- 
ward, the  achromatic  telescope  was  brought  to  perfec- 
tion by  Mr.  Dollond,  a  celebrated  optician  in  London. 

A  perfectly  homogeneous  color  is  very  rarely  to  be 
found,  but  the  tints  of  all  substances  are  most  brilliant 
when  viewed  in  light  of  their  own  color.  The  red  of  a 
wafer  is  much  more  vivid  in  red  than  in  white  light ; 
whereas  if  placed  in  homogeneous  yellow  light,  it  can 
no  longer  appear  red,  because  there  is  not  a  ray  of  red 
in  the  yellow  light.  Were  it  not  that  the  wafer,  like  all 
other  bodies,  whether  colored  or  not,  reflects  white  light 
at  its  outer  surface,  it  would  appear  absolutely  black 
when  placed  in  yellow  light. 

After  looking  steadily  for  a  short  time  at  a  colored 
object,  such  as  a  red  wafer,  on  turning  the  eyes  to  a 
white  substance,  a  green  image  of  the  wafer  appears, 
which  is  called  the  accidental  color  of  red.  All  tints 
have  their  accidental  colors : — thus  the  accidental  color 


160  ACCIDENTAL  COLORS.  SECT.  XIX. 

of  orange  is  blue  ;  that  of  yellow  is  indigo ;  of  green, 
reddish-white  ;  of  blue,  orange-red  ;  of  violet,  yellow ; 
and  of  white,  black  ;  and  vice  versa.  When  the  direct 
and  accidental  colors  are  of  the  same  intensity,  the  acci- 
dental is  then  called  the  complementary  color,  because 
any  two  colors  are  said  to  be  complementary  to  one  an- 
other which  produce  white  when  combined. 

From  recent  experiments  by  M.  Plateau  of  Brussels, 
it  appears  that  two  complementary  colors  from  direct 
impression,  which  would  produce  white  when  combined, 
produce  black,  or  extinguish  one  another  by  their  union, 
when  accidental ;  and  also  that  the  combination  of  all  the 
tints  of  the  solar  spectrum  produces  white  light  if  they 
be  from  a  direct  impression  on  the  eye,  whereas  black- 
ness results  from  a  union  of  the  same  tints  if  they  be 
accidental ;  and  in  every  case  where  the  real  colors  pro- 
duce white  by  their  combination,  the  accidental  colors 
of  the  same  tints  produce  black.  When  the  image  of 
an  object  is  impressed  on  the  retina  only  for  a  few  mo- 
ments, the  picture  left  is  exactly  of  the  same  color  with 
the  object,  but  in  an  extremely  short  time  the  picture 
is  succeeded  by  the  accidental  image.  M.  Plateau  at- 
tributes this  phenomenon  to  a  reaction  of  the  retina  after 
being  excited  by  direct  vision,  so  that  the  accidental  im- 
pression is  of  an  opposite  nature  to  the  corresponding 
direct  impression.  He  conceives,  that  when  the  eye  is 
excited  by  being  fixed  for  a  time  on  a  colored  object,  and 
then  withdrawn  from  the  excitement,  that  it  endeavors 
to  return  to  its  state  of  repose,  but  in  so  doing  that  it 
passes  this  point  and  spontaneously  assumes  an  opposite 
condition,  like  a  spring,  which,  bent  in  one  direction,  in 
returning  to  its  state  of  rest  bends  as  much  the  contrary 
way.  The  accidental  image  thus  results  from  a  partic- 
ular modification  of  the  organ  of  sight,  in  virtue  of  which 
it  spontaneously  gives  us  a  new  sensation  after  it  has 
been  excited  by  direct  vision.  If  the  prevailing  impres- 
sion be  a  very  strong  white  light,  its  accidental  image  is 
not  black,  but,  a  variety  of  colors  in  succession.  Accord- 
ing to  M.  Plateau,  the  retina  offers  a  resistance  to  the 
action  of  light,  which  increases  with  the  duration  of  this 
action ;  whence,  after  looking  intently  at  an  object  for  a 
long  time,  it  appears  to  decrease  in  brilliancy.  The  im- 


SECT.  XX.  INTERFERENCE  OF  LIGHT  161 

agination  has  a  powerful  influence  on  our  optical  impres- 
sions, and  has  been  known  to  revive  the  images  of  highly 
luminous  objects  months,  and  even  years,  afterward. 


SECTION  XX. 


Interference  of  Light—  Undulatory  Theory  of  Light—  Propagation  of  Light 
ings  —  M 
equency 
ton's  Scale  of  Colors  —  Diffraction  of  Light  —  Sir  John  Herschel's  Theory 


gt—  ropagaon  of    ight 

—  Newton'*  Rings  —  Measurement  of  the  Length  of  the  Waves  of  Light, 

Ether  for  each  Color  —  New- 


and of  the  Frequency  of  the  Vibrations  of 
ton's  Scale  of  Colors  —  Diffraction  of  Light 
of  the  Absorption  of  Light  —  Refraction  and  Reflection  of  Light. 

NEWTON  and  most  of  his  immediate  successors  imag- 
ined light  to  be  a  material  substance,  emitted  by  all  self- 
luminous  bodies  in  extremely  minute  particles,  moving 
in  straight  lines  with  prodigious  velocity,  which,  by  im- 
pinging upon  the  optic  nerves,  produce  the  sensation  of 
light.  Many  of  the  observed  phenomena  have  been  ex- 
plained by  this  theory  ;  it  is,  howev,er,  totally  inadequate 
to  account  for  the  following  circumstances. 

When  two  equal  rays  of  red  light,  proceeding  from 
two  luminous  points,  fall  upon  a  sheet  of  "white  paper  in 
a  dark  room,  they  produce  a  red  spot  on  it,  which  will 
be  twice  as  bright  as  either  ray  would  produce  singly, 
provided  the  difference  in  the  lengths  of  the  two'beams, 
from  the  luminous  points  to  the  red  spot  on  the  paper, 
bo  exactly  the  0-0000258th  part  of  an  inch.  The  same 
effect  wiU  take  place  if  the  difference  in  the  lengths  be 
twice,  three  times,  four  times,  &c.  that  quantity.  But 
if  the  difference  in  the  lengths  of  the  two  rays  be  equal 
to  one-half  of  the  0-0000258th  part  of  an  inch,  or  to  its 
H,  2|,  3|,  &c.  part,  the  one  light  will  entirely  extinguish 
the  other,  and  will  produce  absolute  darkness  on  the 
paper  where  the  united  beams  fall.  If  the  difference 
in  the  lengths  of  their  paths  be  equal  to  the  1|,  2|,  3|, 
&c.  of  the  0-0000258th  part  of  an  inch,  the  red  spot 
arising  from  the  combined  beams  will  be  of  the  same 
intensity  which  one  alone  would  produce.  If  violet  light 
be  employed,  the  difference  in  the  lengths  of  the  two 
beams  must  be  equal  to  the  0'0000157th  part  of'an  inch 
in  order  to  produce  the  same  phenomena  ;  and  for  the 
other  colors,  the  difference  must  be  intermediate  be^ 


162  INTERFERENCE  OF  LIGHT.  SECT.  XX- 

tween  the  0-0000258th  and  the  0-0000157th  part  of  an 
inch.  Similar  phenomena  may  be  seen  by  viewing  the 
flame  of  a  candle  through  two  very  fine  slits  in  a  card 
extremely  near  to  one  another  (N.  193)  ;  or  by  admitting 
the  sun's  light  into  a  dark  room  through  a  pin-hole  about 
the  fortieth  of  an  inch  in  diameter,  receiving  the  image 
on  a  sheet  of  white  paper,  and  holding  a  slender  wire  in 
the  light.  Its  shadow  will  be  found  to  consist  of  a  bright 
white  bar  or  stripe  in  the  middle,  with  a  series  of  alter- 
nate black  and  brightly  colored  stripes  on  each  side.  The 
rays  which  bend  round  the  wire  in  two  streams  are  of 
equal  lengths  in  the  middle  stripe;  it  is  consequently 
doubly  bright  from  their  combined  effect ;  but  the  rays 
which  fall  on  the  paper  on  each  side  of  the  bright  stripe, 
being  of  such  unequal  lengths  as  to  destroy  one  another, 
form  black  lines.  On  each  side  of  these  black  lines  the 
rays  are  again  of  such  lengths  as  to  combine  to  form  bright 
stripes,  and  so  on  alternately  till  the  light  is  too  faint  to  be 
visible.  When  any  homogeneous  light  is  used,  such  as 
red,  the  alternations  are  only  black  and  red  ;  but  on  ac- 
count of  the  heterogeneous  nature  of  white  light,  the 
black  lines  alternate  with  vivid  stripes  or  fringes  of  pris- 
matic colors,  arising  from  the  superposition  of  systems 
of  alternate  black  lines  and  lines  of  each  homogeneous 
color.  That  the  alternation  of  black  lines  and  colored 
fringes  actually  does  arise  from  the  mixture  of  the  two 
streams  of  light  which  flow  round  the  wire,  is  proved  by 
their  vanishing  the  instant  one  of  the  streams  is  inter- 
rupted. It  may  therefore  be  concluded,  as  often  as 
these  stripes  of  light  and  darkness  occur,  that  they  are 
owing  to  the  rays  combining  at  certain  intervals  to  pro- 
duce a  joint  effect,  and  at  others  to  extinguish  one 
another.  Now  it  is  contrary  to  all  our  ideas  of  matter 
to  suppose  that  two  particles  of  it  should  annihilate  one 
another  under  any  circumstances  whatever ;  while  on 
the  contrary,  two  opposing  motions  may,  and  it  is  im- 
possible not  to  be  struck  with  the  perfect  similarity  be- 
tween the  interferences  of  small  undulations  of  air  or  of 
water  and  the  preceding  phenomena.  The  analogy  is 
indeed  so  perfect,  that  philosophers  of  the  highest  au- 
thority concur  in  the  supposition  that  the  celestial  regions 
are  filled  with  an  extremely  rare,  imponderable,  and 


S«CT.  XX.  THE  ETHEREAL  MEDIUM.  163 

highly  elastic  medium  or  ether,  whose  particles  are  ca- 
pable of  receiving  the  vibrations  communicated  to  them 
by  self-luminous  bodies,  and  of  transmitting  them  to  the 
optic  nerves,  so  as  to  produce  the  sensation  of  light. 
The  acceleration  in  the  mean  motion  of  Encke's  comet, 
as  well  as  of  the  comet  discovered  by  M.  Biela,  renders 
the  existence  of  such  a  medium  almost  certain.  It  is 
clear  that  in  this  hypothesis,  the  alternate  stripes  of 
light  and  darkness  are  entirely  the  effect  of  the  interfe- 
rence of  the  undulations ;  for  by  actual  measurement, 
the  length  of  a  wave  of  the  mean  red  rays  of  the  solar 
spectrum  is  equal  to  the  0-0000258th  part  of  an  inch ; 
consequently,  when  the  elevation  of  the  waves  combine, 
they  produce  double  the  intensity  of  light  that  each 
would  do  singly ;  and  when  half  a  wave  combines  with 
a  whole, — that  is,  when  the  hollow  of  one  wave  is  filled 
up  by  the  elevation  of  another,  darkness  is  the  result. 
At  intermediate  points  betwsen  these  extremes,  the  in- 
tensity of  the  light  corresponds  to  intermediate  differ- 
ences in  the  lengths  of  the  rays. 

The  theory  of  interferences  is  a  particular  case  of  the 
general  mechanical  law  of  the  superposition  of  small 
motions ;  whence  it  appears  that  the  disturbance  of  a 
particle  of  an  elastic  medium,  produced  by  two  coexis- 
tent undulations,  is  the  sum  of  the  disturbances  which 
each  undulation  would  produce  separately;  conse- 
quently, the  particle  will  move  in  the  diagonal  of  a  par- 
allelogram, whose  sides  are  the  two  undulations.  If, 
therefore,  the  two  undulations  agree  hi  direction,  or 
nearly  so,  the  resulting  motion  will  be  very  nearly  equal 
to  their  sum,  and  in  the  same  direction  :  if  they  nearly 
oppose  one  another,  the  resulting  motion  will  be  nearly 
equal  to  their  difference  ;  and  if  the  undulations  be  equal 
and  opposite,  the  resultant  will  be  zero,  and  the  particle 
will  remain  at  rest. 

The  preceding  experiments,  and  the  inferences  de- 
duced from  them,  which  have  led  to  the  establishment 
of  the  doctrine  of  the  undulations  of  light,  are  the  most 
splendid  memorials  of  our  illustrious  countryman  Dr. 
Thomas  Young,  though  Buy  gens  was  the  first  to  origi- 
nate the  idea. 

It  is  supposed  that  the  particles  of  luminous  bodies 


164  PROPAGATION  OF  LIGHT.  SECT.  XX. 

are  in  a  state  of  perpetual  agitation,  and  that  they  pos- 
sess the  property  of  exciting  regular  vibrations  in  the 
ethereal  medium,  corresponding  to  the  vibrations  of  their 
own  molecules ;  and  that,  on  account  of  its  elastic  nature, 
one  particle  of  the  ether  when  set  in  motion  communi- 
cates its  vibrations  to  those  adjacent,  which  in  succession 
transmit  them  to  those  farther  off ;  so  that  the  primi- 
tive impulse  is  transferred  from  particle  to  particley  and 
the  undulating  motion  darts  through  ether  like  a  wave 
in  water.  Although  the  progressive  motion  of  light  is 
known  by  experience  to  be  uniform  and  in  a  straight 
line,  the  vibrations  of  the  particles  are  always  at  right 
angles  to  the  direction  of  the  ray.  The  propagation  of 
light  is  like  the  spreading  of  waves  in  water  ;  but  if  one 
ray  alone  be  considered,  its  motion  may  be  conceived  by 
supposing  a  rope  of  indefinite  length  stretched  horizon- 
tally, one  end  of  which  is  held  in  the  hand.  If  it  be 
agitated  to  and  fro  at  regular  intervals,  with  a  motion 
perpendicular  to  its  length,  a  series  of  similar  and  equal 
tremors  or  wavps  will  be  propagated  along  it ;  and  if  the 
regular  impulses  be  given  in  a  variety  of  planes,  as  up 
and  down,  from  right  to  left,  and  also  in  oblique  direc- 
tions, the  successive  undulations  will  take  place  in  every 
possible  plane.  An  analogous  motion  in  the  ether, 
when  communicated  to  the  optic  nerves,  would  produce 
the  sensation  of  common  light.  It  is  evident  that  the 
waves  which  flow  from  end  to  end  of  the  cord  in  a  ser- 
pentine form,  are  altogether  different  from  the  perpen- 
dicular vibratory  motion  of  each  particle  of  the  rope, 
which  never  deviates  far  from  a  state  of  rest.  So  in 
ether,  each  particle  vibrates  perpendicularly  to  the  di- 
rection of  the  ray ;  but  these  vibrations  are  totally  dif- 
ferent from,  and  independent  of,  the  undulations  which 
are  transmitted  through  it,  in  the  same  manner  as  the 
vibrations  of  each  particular  ear  of  corn  are  independent 
of  the  waves  that  rush  from  end  to  end  of  a  harvest  field 
when  agitated  by  the  wind. 

The  intensity  of  light  depends  upon  the  amplitude  or 
extent  of  the  vibrations  of  the  particles  of  ether  ;  while 
its  color  depends  upon  their  frequency.  The  time  of 
the  vibration  of  a  particle  of  ether  is  by  theory,  as  the 
length  of  a  wave  directly,  and  inversely  as  its  velocity. 


SECT.  xx.  NEWTON'S  RINGS:  165 

Now,  as  the  velocity  of  light  is  known  to  be  190,000 
miles  in  a  second,  if  the  length  of  the  waves  of  the  dif- 
ferent colored  rays  could  be  measured,  the  number  of 
vibrations  in  a  second  corresponding  to  each  could  be 
computed ;  that  has  been  accomplished  as  follows  : — 
All  transparent  substances  of  a  certain  thickness,  with 
parallel  surfaces,  reflect  and  transmit  white  light ;  but 
if  they  be  extremely  thin,  both  the  reflected  and  trans- 
mitted light  is  colored.  The  vivid  hues  on  soap-bubbles, 
the  iridescent  colors  produced  by  heat  on  polished  steel 
and  copper,  the  fringes  of  color  betweefa  the  laminae  of 
Iceland  spar  and  sulphate  of  lime,  all  consist  of  a  suc- 
cession of  hues  disposed  in  the  same  order,  totally  inde- 
pendent of  the  color  of  the  substance,  and  determined 
solely  by  its  greater  or  less  thickness,  a  circumstance 
which  affords  the  means  of  ascertaining  the  length  of 
the  waves  of  each  colored  ray,  and  the  frequency  of  the 
vibrations  of  the  particles  producing  them.  If  a  plate  of 
glass  be  laid  upon  a  lens  of  almost  imperceptible  curva- 
ture, before  an  open  window;  when  they  are  pressed  to- 
gether a  black  spot  will  be  seen  in  the  point  of  contact, 
surrounded  by  seven  rings  of  vivid  colors,  all  differing 
from  one  another  (N.  194).  In  the  first  ring,  estimated 
from  the  black  spot,  the  colors  succeed  each  other  in  the 
following  order  : — black,  very  faint  blue,  brilliant  white, 
yellow,  orange,  and  red.  They  are  quite  different  in 
the  other  rings,  and  in  the  seventh  the  only  colors  are 
pale  bluish-green  and  very  pale  pink.  That  these  rings 
are  formed  between  the  two  surfaces  in  apparent  con- 
tact may  be  proved  by  laying  a  prism  on  the  lens,  in- 
stead of  the  plate  of  glass,  and  viewing  the  rings  through 
the  inclined  side  of  it  that  is  next  to  the  eye,  which  ar- 
rangement prevents  the  light  reflected  from  the  upper 
surface  mixing  with  that  from  the  surfaces  in  contact,  so 
that  the  intervals  between  the  rings  appear  perfectly 
black, — one  of  the  strongest  circumstances  in  favor  of 
the  undulatory  theory ;  for  although  the  phenomena  of 
the  rings  can  be  explained  by  either  hypothesis,  there 
is  this  material  difference,  that  according  to  the  undu- 
latory theory,  the  intervals  between  the  rings  ought  to 
be  absolutely  black,  which  is  confirmed  by  experiment ; 
whereas  by  the  doctrine  of  emanation  they  ought  to  be 


1C6  NEWTON'S  RINGS.  SECT.  XX. 

half  illuminated,  which  is  not  found  to  be  the  case.  M. 
Fresnel,  whose  opinion  is  of  the  first  authority,  thought 
this  test  conclusive.  It  may  therefore  be  concluded  that 
the  rings  arise  entirely  from  the  interference  of  the 
rays  :  the  light  reflected  from  each  of  the  surfaces  in 
apparent  contact  reaches  the  eye  by  paths  of  different 
lengths,  and  produces  colored  and  dark  rings  alternately, 
according  as  the  reflected  waves  coincide  or  destroy  one 
another.  The  breadths  of  the  rings  are  unequal ;  they 
decrease  in  width,  and  the  colors  become  more  crowded, 
as  they  recede  from  the  center.  Colored  rings  are  also 
produced  by  transmitting  light  through  the  same  ap- 
paratus ;  but  the  colors  are  less  vivid,  and  are  comple- 
mentary to  those  reflected,  consequently  the  central  spot 
is  white. 

The  size  of  the  rings  increases  with  the  obliquity  of 
the  incident  light ;  the  same  color  requiring  a  greater 
thickness  or  space  between  the  glasses  to  produce  it  than 
when  the  light  falls  perpendicularly  upon  them.  Now 
if  the  apparatus  be  placed  in  homogeneous  instead  of 
white  light,  the  rings  will  all  be  of  the  same  color  with 
that  of  the  light  employed.  That  is  to  say,  if  the  light 
be  red,  the  rings  will  be  red  divided  by  black  intervals. 
The  size  of  the  rings  varies  with  the  color  of  the  light. 
They  are  largest  in  red,  and  decrease  in  magnitude  with 
the  succeeding  prismatic  colors,  being  smallest  in  violet 
light. 

Since  one  of  the  glasses  is  plane  and  the  other  spheri- 
cal, it  is  evident  that  from  the  point  of  contact,  the  space 
between  them  gradually  increases  in  thickness  all  round, 
so  that  a  certain  thickness  of  air  corresponds  to  each 
color,  which  in  the  undulatory  system  measures  the  length 
of  the  wave  producing  it  (N.  195).  By  actual  measure- 
ment, Sir  Isaac  Newton  found  that  the  squares  of  the  di- 
ameters of  the  brightest  part  of  each  ring  are  as  the  odd 
numbers,  1,  3,  5, 7,  &c. ;  and  that  the  squares  of. the  diam- 
eters of  the  darkest  parts  are  as  the  even  numbers,  0,  2,  4, 
6,  &c.  Consequently  the  intervals  between  the  glasses 
at  these  points  are  in  the  same  proportion.  If,  then, 
the  thickness  of  the  air  corresponding  to  any  one  color 
could  be  found,  its  thickness  for  all  the  others  would  be 
known.  Now  as  Sir  Isaac  Newton  knew  the  radius  of 


SECT.  XX.          LENGTH  OF  THE  UNDULATIONS.  167 

curvature  of  the  lens,  and  the  actual  breadth  of  the 
rings  in  parts  of  an  inch,  it  was  easy  to  compute  that 
the  thickness  of  air  at  the  darkest  part  of  the  first  ring 
is  the  80oa0  part  of  an  inch,  whence  all  the  others  have 
been  deduced.  As  these  intervals  determine  the  length 
of  the  waves  on  the  undulatory  hypothesis,  it  appears 
that  the  length  of  a  wave  of  the  extreme  red  of  the 
solar  spectrum  is  equal  to  the  00000266th  part  of  an 
inch  ;  that  the  length  of  a  wave  of  the  extreme  violet  is 
equal  to  the  0*00001 67th  part  of  an  inch;  and  as  the 
time  of  a  vibration  of  a  particle  of  ether  producing  any 
particular  color  is  directly  as  the  length  of  a  wave  of  that 
color,  and  inversely  as  the  velocity  of  light,  it  follows 
that  the  molecules  of  ether  producing  the  extreme  red 
of  the  solar  spectrum  perform  458  millions  of  millions 
of  vibrations  in  a  second  ;  and  that  those  producing  the 
extreme  violet  accomplish  727  millions  of  millions  of 
vibrations  in  the  same  time.  The  lengths  of  the  waves 
of  the  intermediate  colors,  and  the  number  of  then* 
vibrations,  being  intermediate  between  these  two,  white 
light,  which  consists  of  all  the  colors,  is  consequently 
a  mixture  of  waves  of  all  lengths  between  the  limits  of 
the  extreme  red  and  violet.  The  determination  of  these 
minute  portions  of  time  and  space,  both  of  which  have 
a  real  existence,  being  the  actual  results  of  measure- 
ment, do  as  much  honor  to  the  genius  of  Newton  as 
that  of  the  law  of  gravitation. 

The  phenomenon  of  the  colored  rings  takes  place  in 
vacuo  as  well  as  in  ah- ;  which  proves  that  it  is  the  dis- 
tance between  the  lenses  alone,  and  not  the  air,  which 
produces  the  colors.  However,  if  water  or  oil  be  put 
between  them,  the  rings  contract,  but  no  other  change 
ensues ;  and  Newton  found  that  the  thickness  of  differ- 
ent media  at  which  a  given  tint  is  seen,  is  in  the  inverse 
ratio  of  their  refractive  indices,  so  that  the  thickness  of 
laminae  which  could  not  otherwise  be  measured,  may  be 
known  by  their  color ;  and  as  the  position  of  the  colors 
in  the  rings  is  invariable,  they  form  a  fixed  standard  of 
comparison  well  known  as  Newton's  scale  of  colors ; 
each  tint  being  estimated  according  to  the  ring  to  which 
it  belongs  from  the  central  spot  inclusively.  Not  only 
the  periodical  colors  which  have  been  described,  but  the 


166-  DIFFRACTION  OF  LIGHT.  SECT.  XX. 

colors  seen  in  thick  plates  of  transparent  substances,  the 
variable  hues  of  feathers,  of  insects'  wings,  mother  of 
pearl,  and  of  striated  substances,  all  depend  Upon  the  same 
principle.  To  these  may  be  added  the  colored  fringes, 
surrounding  the  shadows  of  all  bodies  held  in  an  ex- 
tremely small  beam  of  light,  and  the  colored  rings  sur- 
rounding the  small  beam  itself  when  received  on  a 
screen. 

When  a  very  slender  sunbeam  passing  through   a 
small  pin-hole  into  a  dark  room  is  received  on  a  white 
screen,  or  plate  of  ground  glass,  at  the  distance  of  a  little 
more  than  six  feet,  the  spot  of  light  on  the  screen  is 
larger  than  the  pin-hole ;  and  instead  of  being  bounded 
by  shadow,  it  is  surrounded  by  a  series  of  colored  rings 
separated  by  obscure  intervals.     The  rings  are  more 
distinct  in  proportion  to  the  smallness  of  the  beam  (N. 
196).     When  the  light  is  white,  there  are  seven  rings, 
which  dilate  or  contract  with  the  distance  of  the  screen 
from  the  hole.     As  the  distance  of  the  screen  dimin- 
ishes, the  white  central  spot  contracts  to  a  point  and 
vanishes ;    and  on  approaching  still  nearer,  the  rings 
gradually  close  in  upon  it,  so  that  the  center  assumes 
successively  the  most  intense  and  vivid  hues.     When 
the  light  is  homogeneous,  red,  for  example,  the  rings 
are  alternately  red  and  black,  and  more  numerous :  and 
their  breadth  varies  with  the  color,  being  broadest  in  red 
light  and  narrowest  in  violet.     The  tints  of  the  colored 
fringes  from  white  light,  and  their  obliteration  after  the 
seventh  ring,  arise  from  the  superposition  of  the  differ- 
ent sets  of  fringes  of  all  the  colored  rays.     The  shadows 
of  objects  are  also  bordered  by  colored  fringes  when 
held  in  this  slender  beam  of  light.     If  the  edge  of  a 
knife  or  a  hair,  for  example,  be  held  in  it,  the  rays,  in- 
stead of  proceeding  in  straight  lines  past  its  edge,  are 
bent  when  quite  close  to  it,  and  proceed  from  thence  to 
the  screen  in  curved  lines  called  hyperbolas  ;  so  that  the 
shadow  of  the  object  is  enlarged ;  and  instead  of  being 
at  once  bounded  by  light,  is  surrounded  or  edged  with 
colored  fringes  alternating  with  black  bands,  which  are 
more  distinct  the  smaller  the  pin-hole  (N.  197).     The 
fringes  are  altogether  independent  of  the  form  or  density 
of  the  object,  being  the  same  when  it  is  round  or  pointed, 


8«cr.  XX.  ABSORPTION  OF  LIGHT.  169 

when  of  glass  or  platina.  When  the  rays  which  form 
the  fringes  arrive  at  the  screen,  they  are  of  different 
lengths,  in  consequence  of  the  curved  path  they  follow 
after  passing  the  edge  of  the  object.  The  waves  are 
therefore  in  different  phases  or  states  of  vibration,  and 
either  conspire  to  form  colored  fringes  or  destroy  one 
another  in  the  obscure  intervals.  The  colored  fringes 
bordering  the  shadows  of  objects  were  first  described  by 
Grirnaldi  in  1665;  but  besides  these  he  noticed  that 
there  are  others  within  the  shadows  of  slender  bodies 
exposed  to  a  small  sunbeam,  a  phenomenon  which  has 
already  been  mentioned  to  have  afforded  Dr.  Young  the 
means  of  proving  beyond  all  controversy,  that  colored 
rings  are  produced  by  the  interference  of  light. 

It  may  be  concluded,  that  material  substances  derive 
their  colors  from  two  different  causes :  some  from  the 
law  of  interference,  such  as  iridescent  metals,  peacocks' 
feathers,  &c.;  others  from  the  unequal  absorption  of 
the  rays  of  white  light,  such  as  vermilion,  ultramarine, 
blue,  or  green  cloth,  flowers,  and  the  greater  number  of 
colored  bodies.  The  latter  phenomena  have  been  con- 
sidered extremely  difficult  to  reconcile  with  the  undula- 
tory  theory  of  light,  and  much  discussion  has  arisen  as 
to  what  becomes  of  the  absorbed  rays.  But  that  em- 
barrassing question  has  been  ably  answered  by  Sir  John 
Herschel  in  a  most  profound  paper,  On  the  Absorption 
of  Light  by  colored  Media,  and  cannot  be  better  given 
than  in  his  own  words.  It  must  however  be  premised, 
that  as  all  transparent  bodies  are  traversed  by  light, 
they  are  presumed  to  be  permeable  to  the  ether.  He 
says,  "  Now,  as  regards  only  the  general  feet  of  the  ob- 
struction and  ultimate  extinction  of  light  in  its  passage 
through  gross  media,  if  we  compare  the  corpuscular  and 
undulatory  theories,  we  shall  find  that  the  former  ap- 
peals to  our  ignorance,  the  latter  to  our  knowledge,  for 
its  explanation  of  the  absorptive  phenomena.  In  at- 
tempting to  explain  the  extinction  of  light  on  the  corpus- 
cular doctrine,  we  have  to  account  for  the  light  so  extin- 
guished as  a  material  body,  which  we  must  not  suppose 
annihilated.  It  may  however  be  transformed;  and 
among  the  imponderable  agents,  heat,  electricity,  &c., 
it  may  be  that  we  are  to  search  for  the  light  which  has 


170  ABSORPTION  01'  LIGHT  SECT.  XX. 

become  thus  comparatively  stagnant.  The  heating 
power  of  the  solar  rays  gives  a  primd  facie  plausibility 
to  the  idea  of  the  transformation  of  light  into  heat  by 
absorption.  But  when  we  come  to  examine  the  matter 
more  nearly,  we  find  it  encumbered  on  all  sides  with 
difficulties.  How  is  it,  for  instance,  that  the  most  lu- 
minous rays  are  not  the  most  calorific ;  but  that  on  the 
contrary,  the  calorific  energy  accompanies,  in  its  great- 
est intensity,  rays  which  possess  comparatively  feeble 
illuminating  powers  ?  These  and  other  questions  of  a 
similar  nature  may  perhaps  admit  of  answer  in  a  more 
advanced  state  of  our  knowledge  ;  but  at  present  there 
is  none  obvious.  It  is  not  without  reason,  therefore, 
that  the  question  '  What  becomes  of  light  ?'  which  ap- 
pears to  have  been  agitated  among  the  photologists  of 
the  last  century,  has  been  regarded  as  one  of  consider- 
able importance  as  well  as  obscurity  by  the  corpuscular 
philosophers.  On  the  other  hand,  the  answer  to  this 
question,  afforded  by  the  undulatory  theory  of  light,  is 
simple  and  distinct.  The  question,  '  What  becomes  of 
light  ?'  merges  in  the  more  general  one,  '  What  becomes 
of  motion  ? '  And  the  answer,  on  dynamical  principles, 
is,  that  it  continues  forever.  No  motion  is,  strictly 
speaking,  annihilated  ;  but  it  may  be  divided,  and  the 
divided  parts  made  to  oppose  and,  in  effect,  destroy  one 
another.  A  body  struck,  however  perfectly  elastic, 
vibrates  for  a  time,  and  then  appears  to  sink  into  its 
original  repose.  But  this  apparent  rest  (even  abstract- 
ing from  the  inquiry  that  part  of  the  motion  which  may 
be  conveyed  away  by  the  ambient  air)  is  nothing  else 
than  a  state  of  subdivided  and  mutually  destroying  mo- 
tion, in  which  every  molecule  continues  to  be  agitated 
by  an  indefinite  multitude  of  internally  reflected  waves, 
propagated  through  it  in  every  possible  direction,  from 
eveiy  point  in  its  surface  on  which  they  successively 
impinge.  The  superposition  of  such  waves  will,  it  is 
easily  seen,  at  length  operate  their  mutual  destruction, 
which  will  be  the  more  complete  the  more  irregular  the 
figure  of  the  body,  and  the  greater  the  number  of  inter- 
nal reflections."  Thus  Sir  John  Herschel,  by  referring 
the  absorption  of,  light  to  the  subdivision  and  mutual 
destruction  of  the  vibrations  of  ether  in  the  interior  of 


S«CT.  XX.  TRANSMISSION  OP  LIGHT  171 

bodies,  brings  another  class  of  phenomena  under  the 
laws  of  the  undulatory  theory. 

The  ethereal  medium  pervading  space  is  supposed  to 
penetrate  all  material  substances,  occupying  the  inter- 
stices between  their  molecules;  but  in  the  interior  of 
refracting  media  it  exists  in  a  state  of  less  elasticity 
compared  with  ks  density  in  vacuo ;  and  the  more 
refractive  the  medium,  the  less  the  elasticity  of  the 
ether  within  it.  Hence  the  waves  of  light  are  trans- 
mitted with  less  velocity  in  such  media  as  glass  and 
water  than  in  the' external  ether.  As  soon  as  a  ray  of 
light  reaches  the  surface  of  a  diaphanous  reflecting  sub- 
stance, for  example  a  plate  of  glass,  it  communicates  its 
undulations  to  the  ether  next  in  contact  with  the  surface, 
which  thus  becomes  a  new  center  of  motion,  and  two 
hemispherical  waves  are  propagated  from  each  point  of 
this  surface ;  one  of  which  proceeds  forward  into  the 
interior  of  the  glass,  with  E  less  velocity  than  the  inci- 
dent waves  ;  and  the  other  is  transmitted  back  into  the 
air,  with  a  velocity  equal  to  that  with  which  -it'  came 
(N.  198).  Thus  when  refracted,  the  light  moves  with 
a  different  velocity  without  and  within  the  glass ;  when 
reflected,  the  ray  comes  and  goes  with  the  same  ve- 
locity. The  particles  of  ether  without  the  glass,  which 
communicate  their  motions  to  the  particles  of  the  dense 
and  less  elastic  ether  within  it,  are  analogous  to  small 
elastic  balls  striking  large  ones  ;  for  some  of  the  motion 
will  be  communicated  to  the  large  balls,  and  the  small 
ones  will  be  reflected.  The  first  would  cause  the 
refracted  wave ;  and  the  last  the  reflected.  Conversely, 
when  the  light  passes  from  glass  to  air,  the  action  is 
similar  to  large  balls  striking  small  ones.  The  small 
balls  receive  a  motion  which  would  cause  the  refracted 
ray,  and  the  part  of  the  motion  retained  by  the  large 
ones  would  occasion  the  reflected  wave ;  so  that  when 
light  passes  through  a  plate  of  glass  or  of  any  other 
medium  differing  in  density  from  the  air,  there  is  a 
reflection  at  both  surfaces ;  but  this  difference  exists 
between  the  two  reflections,  that  one  is  caused  by  a 
vibration  in  the  same  direction  with  that  of  the  incident 
ray,  and  the  other  by  a  vibration  in  the  opposite  direction. 

A  single  wave  of  air  or  ether  would  not  produce  the 


172  ACTION  OF  LIGHT  ON  THE  RETINA.    SECT.  XXI. 

sensation  of  sound  or  light.  In  order  to  excite  vision, 
the  vibrations  of  the  molecules  of  ether  must  be  regular, 
periodical,  and  very  often  repeated;  and  as  the  ear 
continues  to  be  agitated  for  a  short  time  after  the  im- 
pulse by  which  alone  a  sound  becomes  continuous,  so 
also  the  fibres  of  the  retina,  according  to  M.  d'Arcet, 
continue  to  vibrate  for  about  the  eighth  part  of  a  second, 
after  the  exciting  cause  has  ceased.  Every  one  must 
have  observed,  when  a  strong  impression  is  made  by  a 
bright  light,  that  an  object  remains  visible  for  a  short 
time  after  shutting  the  eyes,  which  is  supposed  to  be 
in  consequence  of  the  continued  vibrations  of  the  fibres 
of  the  retina.  Occasionally  the  retina  becomes  insen- 
sible to  feebly  illuminated  objects  when  continuously 
presented.  If  the  eye  be  turned  aside  for  a  moment, 
the  object  becomes  again  visible.  It  is  probably  on  this 
account  that  the  owl  makes  so  peculiar  a  motion  with 
its  head  when  looking  at  objects  in  the  twilight.  It  is 
quite  possible  that  many  vibrations  may  be  excited  in 
the  ethereal  medium  incapable  of  producing  undulations 
in  the  fibres  of  the  human  retina,  which  yet  have  a 
powerful  effect  on  those  of  other  animals  or  of  insects. 
Such  may  receive  luminous  impressions  of  which  wo 
are  totally  unconscious,  and  at  the  same  time  they  may 
be  insensible  to  the  light  and  colors  which  affect  our 
eyes  ;  their  perceptions  beginning  where  ours  end. 


SECTION  XXL 

Polarization  of  Light— Defined— Polarization  by  Refraction— Properties  of 
the  Tourmaline— Double  Refraction— All  doubly  Refracted  Light  is 
Polarized — Properties  of  Iceland  Spar — Tourmaline  absorbs  one  of  the 
two  Refracted  Rays — Undulations  of  Natural  Light — Undulations  of 
Polarized  Light— The  Optic  Axes  of  Crystals— M.  Fresnel's  Discoveries 
on  the  Rays  passing  along  the  Optic  Axis — Polarization  by  Reflection. 

IN  giving  a  sketch  of  the  constitution  of  light,  it  is 
impossible  to  omit  the  extraordinary  property  of  its  po- 
larization, "the  phenomena  of  which,"  Sir  John  Her- 
schel  says,  "are  so  singular  and  various,  that  to  one 
who  has  only  studied  the  common  branches  of  physical 
optics  it  is  liko  entering  into  a  new  world,  so  splendid 


SECT.  XXI.       POLARIZATION  BY  BEFB ACTION.  173 

as  to  render  it  one  of  the  most  delightful  branches  of 
experimental  inquiry,  and  so  fertile  in  the  views  it  lays 
open  of  the  constitution  of  natural  bodies,  and  the 
minuter  mechanism  of  the  universe,  as  to  place  it  in  the 
very  first  rank  of  the  physico-mathematical  sciences, 
which  it  maintains  by  the  rigorous  application  of  geome- 
trical reasoning  its  nature  admits  and  requires. 

Light  is  said  to  be  polarized,  which,  by  being  once 
reflected  or  refracted,  is  rendered  incapable  of  being 
again  reflected  or  refracted  at  certain  angles.  In  gene- 
ral, when  a  ray  of  light  is  reflected  from  a  pane  of  plate- 
glass,  or  any  other  substance,  it  may  be  reflected  a 
second  time  from  another  surface,  and  it  will  also  pass 
freely  through  transparent  bodies.  But  if  a  ray  of  light 
be  reflected  from  a  pane  of  plate-glass  at  an  angle  of 
57°,  it  is  rendered  totally  incapable  of  reflection  at  the 
surface  of  another  pane  of  glass  in  certain  definite  po- 
sitions, but  it  will  be  completely  reflected  by  the  second 
pane  in  other  positions.  It  likewise  loses  the  property 
of  penetrating  transparent  bodies  in  particular  positions, 
while  it  is  freely  transmitted  by  them  in  others.  Light 
so  modified  as  to  be  incapable  of  reflection  and  trans- 
mission in  certain  directions,  is  said  to  be  polarized. 
This  name  was  originally  adopted  from  an  imaginary 
analogy  in  the  arrangement  of  the  particles  of  light  on 
the  corpuscular  doctrine  to  the  poles  of  a  magnet,  and  is 
still  retained  in  the  undulatory  theory. 

Light  may  be  polarized  by  reflection  from  any  polished 
surface,  and  the  same  property  is  also  imparted  by  re- 
fraction. It  is  proposed  to  explain  these  methods  of 
polarizing  light,  to  give  a  short  account  of  its  most  re- 
markable properties,  and  to  endeavor  to  describe  a  few 
of  the  splendid  phenomena  it  exhibits. 

If  a  brown  tourmaline,  which  is  a  mineral  generaDy 
crystalized  in  the  form  of  a  long  prism,  be  cut  longitu- 
dinally, that  is,  parallel  to  the  axis  of  the  prism,  into 
plates  about  the  thirtieth  of  an  inch  in  thickness,  and 
the  surfaces  polished,  luminous  objects  may  be  seen 
through  them,  as  through  plates  of  colored  glass.  The 
axis  of  each  plate  is  in  its  longitudinal  section  parallel  to 
the  axis  of  the  prism  whence  it  was  cut  (N.  199).  If 
pne  of  these  plates  be  held  perpendicularly  between 


174  POLARIZATION  BY  REFRACTION.      SECT.  XXI. 

the  eye  and  a  candle,  and  turned  slowly  round  in  its 
own  plane,  no  change  will  take  place  in  the  image  of 
the  candle.  But  if  the  plate  be  held  in  a  fixed  position, 
with  its  axis  or  longitudinal  section  vertical,  when  a 
second  plate  of  tourmaline  is  interposed  between  it  and 
the  eye,  parallel  to  the  first,  and  turned  slowly  round  in 
its  own  plane,  a  remarkable  change  will  be  found  to 
have  taken  place  in  the  nature  of  the  light.  For  the 
image  of  the  candle  will  vanish  and  appear  alternately 
at  every  quarter  revolution  of  the  plate,  varying  through 
all  degrees  of  brightness  down  to  total,  or  almost  total 
evanescence,  and  then  increasing  again  by  the  same  de- 
grees as  it  had  before  decreased.  These  changes  de- 
pend upon  the  relative  positions  of  the  plates.  When 
the  longitudinal  sections  of  the  two  plates  are  parallel, 
the  brightness  of  the  image  is  at  its  maximum ;  and 
when  the  axes  of  the  sections  cross  at  right  angles,  the 
image  of  the  candle  vanishes.  Thus  the  light,  in  pass- 
ing through  the  first  plate  of  tourmaline,  has  acquired  a 
property  totally  different  from  the  direct  light  of  the 
candle.  The  direct  light  would  have  penetrated  the 
second  plate  equally  well  in  all  directions,  whereas  the 
refracted  ray  will  only  pass  through  it  in  particular  po- 
sitions, and  is  altogether  incapable  of  penetrating  it  in 
others.  The  refracted  ray  is  polarized  in  its  passage 
through  the  first  tourmaline,  and  experience  shows  that 
it  never  loses  that  property,  unless  when  acted  upon  by 
a  new  substance.  Thus,  one  of  the  properties  of  po- 
larized light  is  the  incapability  of  passing  through  a  plate 
of  tourmaline  perpendicular  to  it,  in  certain  positions, 
and  its  ready  transmission  in  other  positions  at  right 
angles  to  the  former. 

Many  other  substances  have  the  property  of  polar- 
izing light.  If  a  ray  of  light  falls  upon  a  transparent 
medium,  which  has  the  same  temperature,  density,  and 
structure  throughout  every  part,  as  fluids,  gases,  glass, 
&c.,  and  a  few  regularly  crystalized  minerals,  it  is  re- 
fracted into  a  single  pencil  of  light  by  the  laws  of  ordi- 
nary refraction,  according  to  which  the  ray,  passing 
through  the  refracting  surface  from  the  object  to  the 
eye,  never  quits  a  plane  perpendicular  to  that  surface. 
Almost  all  other  bodies,  such  as  the  greater  number  of 


S«cr.  XXI.  DOUBLE  REFRACTION.  175 

crystaKzed  minerals,  animal  and  vegetable  substances, 
gums,  resins,  jellies,  and  all  solid  bodies  having  unequal 
tensions,  whether  from  unequal  temperature  or  pres- 
sure, possess  the  property  of  doubling  the  image  or  ap- 
pearance of  an  object  seen  through  them  in  certain 
directions.  Because  a  ray  of  natural  light  falling  upon 
them  is  refracted  into  two  pencils,  which  move  with  dif- 
ferent velocities,  and  are  more  or  less  separated,  accord- 
ing to  the  nature  of  the  body  and  the  direction  of  the 
incident  ray.  Whenever  a  ray  of  natural  light  is  thus 
divided  into  two  pencils  in  its  passage  through  a  sub- 
stance, both  of  the  transmitted  rays  are  polarized.  Ice- 
land spar,  a  carbonate  of  lime,  which  by  its  natural 
cleavage  may  be  split  into  the  form  of  a  rhombohedron, 
possesses  the  property  of  double  refraction  in  an  emi- 
nent degree,  as  may  be  seen  by  pasting  a  piece  of  paper 
with  a  large  pin-hole  in  it,  on  the  side  of  the  spar  far- 
thest from  the  eye.  The  hole  will  appear  double  when 
held  to  the  light  (N.  200).  One  of  these  pencils  is  re- 
fracted according  to  the  same  law  as  in  glass  or  water, 
never  quitting  the  plane  perpendicular  to  the  refracting 
surface,  and  is  therefore  called  the  ordinary  ray.  But 
the  other  does  quit  the  plane,  being  refracted  according 
to  a  different  and  much  more  complicated  law,  and  on 
that  account  is  called  the  extraordinary  ray.  For  the 
same  reason  one  image  is  called  the  ordinary,  and  the 
other  the  extraordinary  image.  When  the  spar  is  turned 
round  in  the  same  plane,  the  extraordinary  image  of  the 
hole  revolves  about  the  ordinary  image  which  remains 
fixed,  both  being  equally  bright.  But  if  the  spar  be  kept 
in  one  position  and  viewed  through  a  plate  of  tourma- 
line, it  will  be  found  that  as  the  tourmaline  revolves,  the 
images  vary  in  their  relative  brightness — one  increases 
in  intensity  till  it  arrives  at  a  maximum,  at  the  same 
time  that  the  other  diminishes  till  it  vanishes,  and  so  on 
alternately  at  each  quarter  revolution,  proving  both  rays 
to  be  polarized.  For  in  one  position  the  tourmaline 
transmits  the  ordinary  ray,  and  reflects  the  extraordi- 
nary; and  after  revolving  90°,  the  extraordinary  ray  is 
transmitted,  and  the  ordinary  ray  is  reflected.  Thus 
another  property  of  polarized  light  is,  that  it  cannot  be 
divided  into  two  equal  pencils  by  double  refraction,  in 


176  DOUBLE  REFRACTION.  SECT.  XXI. 

positions  of  the  doubly  refracting  bodies  in  which  a  ray 
of  common  light  would  be  so  divided. 

Were  tourmaline  like  other  doubly  refracting  bodies, 
each  of  the  transmitted  rays  would  be  double  ;  but  that 
mineral  when  of  a  certain  thickness,  after  separating  the 
light  into  two  polarized  pencils,  absorbs  that  which  un- 
dergoes ordinary  refraction,  and  consequently  shows 
only  one  image  of  an  object.  On  this  account,  tourma- 
line is  peculiarly  fitted  for  analyzing  polarized  light, 
which  shows  nothing  remarkable  till  viewed  through  it 
or  something  equivalent. 

The  pencils  of  light,  on  leaving  a  double  refracting 
substance*  are  parallel ;  and  it  is  clear  from  the  prece- 
ding experiments,  that  they  are  polarized  in  planes  at 
right  angles  to  each  other  (N.  201).  But  that  will  be 
better  understood  by  considering  the  change  produced 
in  common  light  by  the  action  of  the  polarizing  body.  It 
has  been  shown  that  the  undulations  of  ether,  which 
produce  the  sensation  of  common  light,  are  performed 
in  every  possible  plane,  at  right  angles  to  the  direction 
in  which  the  ray  is  moving.  But  the  case  is  veiy  dif- 
ferent after  the  ray  has  passed  through  a  doubly  refract- 
ing substance,  like  Iceland  spar.  The  light  then  pro- 
ceeds in  two  parallel  pencils,  whose  undulations  are  still 
indeed  transverse  to  the  direction  of  the  rays,  but  they 
are  accomplished  in  planes  at  right  angles  to  one  an- 
other, analogous  to  two  parallel  stretched  cords,  one  of 
which  performs  its  undulations  only  in  a  horizontal 
plane,  and  the  other  in  a  vertical  or  upright  plane  (N. 
201).  Thus  the  polarizing  action  of  Iceland  spar  and 
of  all  doubly  refracting  substances  is,  to  separate  a  ray 
of  common  light,  whose  waves  or  undulations  are  in 
every  plane,  into  two  parallel  rays,  whose  waves  or  un- 
dulations lie  in  planes  at  right  angles  to  each  other.  The 
ray  of  common  light  may  be  assimilated  to  a  round  rod, 
whereas  the  two  polarized  rays  are  like  two  parallel 
long  flat  rulers,  one  of  which  is  laid  horizontally  on  its 
broad  surface,  and  the  other  horizontally  on  its  edge. 
The  alternate  transmission  and  obstruction  of  one  of 
these  flattened  beams  by  the  tourmaline  is  similar  to  the 
facility  with  which  a  card  may  be  passed  between  the 
bars  of  a  grating  or  wires  of  a  cage,  if  presented  edge- 


S*cr.  XXI.        THE  OPTIC  AXES  OP  CRYSTALS.  177 

ways,  and  the  impossibility  of  its  passing  in  a  transverse 
direction. 

Although  it  generally  happens  that  a  ray  of  light,  in 
passing  through  Iceland  spar,  is  separated  into  two  po- 
larized rays,  yet  there  is  one  direction  along  which  it  is 
refracted  in  one  ray  only,  and  that  according  to  the  or- 
dinary law.  This  direction  is  called  the  optic  axis 
(N.  202).  Many  crystals  and  other  substances  have 
two  optic  axes,  inclined  to  each  other,  along  which  a 
ray  of  light  is  transmitted  in  one  pencil  by  the  law  of 
ordinary  refraction.  The  extraordinary  ray  is  some- 
times refracted  toward  the  optic  axis,  as  in  quartz,  zir- 
con, ice,  &c.,  which  are  therefore  said  to  be  positive 
crystals ;  but  when  it  is  bent  from  the  optic  axis,  as  in 
Iceland  spar,  tourmaline,  emerald,  beryl,  &c.,  the  crys- 
tals are  negative,  which  is  the  most  numerous  class. 
The  ordinary  ray  moves  with  uniform  velocity  within  a 
doubly  refracting  substance,  but  the  velocity  of  the  ex- 
traordinary ray  varies  with  the  position  of  the  ray  rela- 
tively to  the  optic  axis,  being  a  maximum  when  its  mo- 
tion within  the  crystal  is  at  right  angles  to  the  optic  axis, 
and  a  minimum  when  parallel  to  it.  Between  these  ex- 
tremes its  velocity  varies  according  to  a  determinate  law. 

It  has  been  inferred  from  the  action  of  Iceland  spar 
on  light,  that  in  all  doubly  refracting  substances,  one  only 
of  two  rays  is  turned  aside  from  the  plane  of  ordinary 
refraction,  while  the  other  follows  the  ordinary  law ;  and 
the  great  difficulty  of  observing  the  phenomena  tended 
to  confirm  that  opinion.  M.  Fresnel,  however,  proved 
by  a  most  profound  mathematical  inquiry,  a  priori,  that 
the  extraordinary  ray  must  be  wanting  in  glass  and  other 
uncrystalized  substances,  and  that  it  must  necessarily 
exist  in  carbonate  of  lime,  quartz,  and  other  bodies  hav- 
ing one  optic  axis,  but  that  in  a  numerous  class  of  sub- 
stances which  possess  two  optic  axes,  both  rays  must 
undergo  extraordinary  refraction,  and  consequently  that 
both  must  deviate  from  their  original  plane,  and  these 
results  have  been  perfectly  confirmed  by  subsequent 
experiments.  This  theory  of  refraction,  which  for  gen- 
eralization is  perhaps  only  inferior  to  the  law  of  gravita- 
tion, has  enrolled  the  name  of  Fresnel  among  those 
which  pass  not  away,  and  makes  his  early  loss  a  subject 

12 

^g 


178  POLARIZATION  NY  PLATES  OF  GLASS.    SECT,  XXI. 

of  deep  regret  to  all  who  take  an  interest  in  the  higher 
paths  of  scientific  research. 

When  a  beam  of  common  light  is  partly  reflected  at, 
and  partly  transmitted  through,  a  transparent  surface, 
the  reflected  and  refracted  pencils  contain  equal  quanti- 
ties of  polarized  light,  and  their  planes  of  polarization 
are  at  right  angles  to  one  another  :  hence  a  pile  of  panes 
of  glass  will  give  a  polarized  beam  by  refraction.  For  if 
a  ray  of  common  light  pass  through  them,  part  of  it 
will  be  polarized  by  the  first  plate,  the  second  plate  will 
polarize  a  part  of  what  passes  through  it,  and  the  rest 
will  do  the  same  in  succession,  till  the  whole  beam  is 
polarized,  except  what  is  lost  by  reflection  at  the  dif- 
ferent surfaces,  or  by  absorption.  This  beam  is  polar- 
ized in  a  plane  at  right  angles  to  the  plane  of  reflection, 
that  is,  at  right  angles  to  the  plane  passing  through  the 
incident  and  reflected  ray  (N.  203). 

By  far  the  most  convenient  way  of  polarizing  light  is 
by  reflection.  A  plane  of  plate-glass  laid  upon  a  piece 
of  black  cloth,  on  a  table  at  an  open  window,  will  appear 
of  a  uniform  brightness  from  the  reflection  of  the  sky 
or  clouds.  But  if  it  be  viewed  through  a  plate  of  tour- 
maline, having  its  axis  vertical,  instead  of  being  illumi- 
nated as  before,  it  will  be  obscured  by  a  large  cloudy 
spot,  having  its  center  quite  dark,  which  will  readily  be 
found  by  elevating  or  depressing  the  eye,  and  will  only 
be  visible  when  the  angle  of  incidence  is  57°,  that  is, 
when  the  line  from  the  eye  to  the  center  of  the  black 
spot  makes  an  angle  of  33°  with  the  surface  of  the  re- 
flector (N.  204).  When  the  tourmaline  is  turned  round 
in  its  own  plane,  the  dark  cloud  will  diminish,  and  en- 
tirely vanish  when  the  axis  of  the  tourmaline  is  horizon- 
tal, and  then  every  part  of  the  surface  of  the  glass  will 
be  equally  illuminated.  As  the  tourmaline  revolves,  the 
cloudy  spot  will  appear  and  vanish  alternately  at  every 
quarter  revolution.  Thus,  when  a  ray  of  light  is  inci- 
dent on  a  pane  of  plate-glass  at  an  angle  of  57°,  the  re- 
flected ray  is  rendered  incapable  of  penetrating  a  plate 
of  tourmaline,  whose  axis  is  in  the  plane  of  incidence. 
Consequently  it  has  acquired  the  same  character  as  if 
it  had  been  polarized  by  transmission  through  a  plate 
of  tourmaline,  with  its  axis  at  right  angles  to  the  plane 


S*tT.  XXI.         POLARIZATION  BY  REFLECTION.  179 

of  reflection.  It  is  found  by  experience  that  this  polar- 
ized ray  is  incapable  of  a  second  reflection  at  certain 
angles  and  in  certain  positions  of  the  incident  plane. 
For  if  another  pane  of  plate-glass  having  one  surface 
blackened,  be  so  placed  as  to  make  an  angle  of  33°  with 
the  reflected  ray,  the  image  of  the  first  pane  will  be  re- 
flected in  its  surface,  and  will  be  alternately  illuminated 
and  obscured  at  every  quarter  revolution  of  the  black- 
ened pane,  according  as  the  plane  of  reflection  is  parallel 
or  perpendicular  to  the  plane  of  polarization.  Since 
this  happens  by  whatever  means  the  light  has  been 
polarized,  it  evinces  another  general  property  of  polar- 
ized light,  which  is,  that  it  is  incapable  of  reflection  in  a 
plane  at  right  angles  to  the  plane  of  polarization. 

All  reflecting  surfaces  are  capable  of  polarizing  light, 
but  the  angle  of  incidence  at  which  it  is  completely 
polarized  is  different  in  each  substance  (N.  205).  It 
appears  that  the  angle  for  plate-glass  is  57°  ;  in  crown- 
glass  it  is  56°  55',  and  no  ray  will  be  completely  polar- 
ized by  water,  unless  the  angle  of  incidence  be  53°  11'. 
The  angles  at  which  different  substances  polarize  light 
are  determined  by  a  very  simple  and  elegant  law,  dis- 
covered by  Sir  David  Brewster,  "  That  the  tangent  of 
the  polarizing  angle  for  any  medium  is  equal  to  the  sine 
of  the  angle  of  incidence  divided  by  the  sine  of  the  angle 
of  refraction  of  that  medium."  Whence  also  the  re- 
fractive power  even  of  an  opaque  body  is  known  when 
its  polarizing  angle  has  been  determined. 

Metallic  substances,  and  such  as  are  of  high  refractive 
powers,  like  the  diamond,  polarize  imperfectly. 

If  a  ray  polarized  by  refraction  or  by  reflection  from 
any  substance  not  metallic,  be  viewed  through  a  piece 
of  Iceland  spar,  each  image  will  alternately  vanish  and 
reappear  at  every  quarter  revolution  of  the  spar,  whether 
it  revolves  from  right  to  left,  or  from  left  to  right ;  which 
shows  that  the  properties  of  the  polarized  ray  are  sym- 
metrical on  each  side  of  the  plane  of  polarization. 

Although  there  be  only  one  angle  in  each  substance 
at  which  light  is  completely  polarized  by  one  reflection, 
yet  it  may  be  polarized  at  any  angle  of  incidence  by  a 
sufficient  number  of  reflections.  For  if  a  ray  falls  upon 
the  upper  surface  of  a  pile  of  plates  of  glass  at  an  angle 


180  COLORED  IMAGES.  SfccT.  XXII. 

greater  or  less  than  a  polarizing  angle,  a  part  only  of 
the  reflected  ray  will  be  polarized,  but  a  part  of  what  is 
transmitted  will  be  polarized  by  reflection  at  the  sur- 
face of  the  second  plate,  part  at  the  third,  and  so  on  till 
the  whole  is  poralized.  This  is  the  best  apparatus  ;  but 
one  plate  of  glass  having  its  inferior  surface  blackened, 
or  even  a  polished  table,  will  answer  the  purpose. 

''"  ' 


SECTION  XXII. 

Phenomena  exhibited  by  the  passage  of  Polarized  Light  through  Mica  and 
Sulphate  of  Lime — The  Colored  Images  produced  by  Polarized  Light 
passing  through  Crystals  having  one  and  two  Optic  Axes — Circular 
Polarization — Elliptical  Polarization — Discoveries  of  MM.  Biot,  Fresnel, 
and  Professor  Airy — Colored  Images  produced  by  the  Interference  of 
Polarized  Rays. 

SUCH  is  the  nature  of  polarized  light  and  of  the  laws 
it  follows.  But  it  is  hardly  possible  to  convey  an  idea  of 
the  splendor  of  the  phenomena  it  exhibits  under  circum- 
stances which  an  attempt  will  now  be  made  to  describe. 

If  light  polarized  by  reflection  from  a  pane  of  glass  be 
viewed  through  a  plate  of  tourmaline,  with  its  longitudi- 
nal section  vertical,  an  obscure  cloud,  with  its  center 
totally  dark,  will  be  seen  on  the  glass.  Now  let  a  plate 
of  mica,  uniformly  about  the  thirtieth  of  an  inch  in  thick- 
ness, be  interposed  between  the  tourmaline  and  the 
glass  ;  the  dark  spot  will  instantly  vanish,  and  instead  of 
it,  a  succession  of  the  most  gorgeous  colors  will  appear, 
varying  with  every  inclination  of  the  mica,  from  the 
richest  reds,  to  the  most  vivid  greens,  blues,  and  purples 
(N.  206).  That  they  may  be  seen  in  perfection,  the 
mica  must  revolve  at  right  angles  to  its  own  plane. 
When  the  mica  is  turned  round  in  a  plane  perpendicu- 
lar to  the  polarized  ray,  it  will  be  found  that  there  are 
two  lines  in  it  where  the  colors  entirely  vanish.  These 
are  the  optic  axes  of  the  mica,  which  is  a  doubly  refract- 
ing substance,  with  two  optic  axes,  along  which  light  is 
refracted  in  one  pencil. 

No  colors  are  visible  in  the  mica,  whatever  its  position 
may  be  with  regard  to  the  polarized  light,  without  the 
aid  of  the  tourmaline,  which  separates  the  transmitted 
ray  into  two  pencils  of  colored  light  complementary  to 


SKCT.  XXII.  COLORED  IMAGES.  181 

one  another,  that  is,  which  taken  together  would  make 
white  light.  One  of  these  it  absorbs,  and  transmits  the 
other;  it  is  therefore  called  the  analyzing  plate.  The 
truth  of  this  will  appear  more  readily,  if  a  film  of  sul- 
phate of  lime  between  the  twentieth  and  sixtieth  of  an 
inch  thick  be  used  instead  of  the  mica.  When  the  film 
is  of  uniform  thickness,  only  one  color  will  be  seen  when 
it  is  placed  between  the  analyzing  plate  and  the  reflect- 
ing glass ;  as,  for  example,  red.  But  when  the  tourma- 
line revolves,  the  red  will  vanish  by  degrees  till  the  film 
is  colorless ;  then  it  will  assume  a  green  hue,  which 
will  increase  and  arrive  at  its  maximum  when  the  tour- 
maline has  turned  through  ninety  degrees ;  after  that 
the  green  will  vanish  and  the  red  will  reappear,  alter- 
nating at  each  quadrant.  Thus  the  tourmaline  separ- 
ates the  light  which  has  passed  through  the  film  into  a 
red  and  a  green  pencil ;  in  one  position  it  absorbs  the 
green  and  lets  the  red  pass,  and  in  another  it  absorbs 
the  red  and  transmits  the  green.  This  is  proved  by 
analyzing  the  ray  with  Iceland  spar  instead  of  tourmaline ; 
for  since  the  spar  does  not  absorb  the  light,  two  images 
of  the  sulphate  of  lime  will  be  seen,  one  red  and  the 
other  green,  and  these  exchange  colors  every  quarter 
revolution  of  the  spar,  the  red  becoming  green,  and  the 
green  red^  and  where  the  images  overlap,  the  color  is 
white,  proving  the  red  and  green  to  be  complementary 
to  each  other.  The  tint  depends  on  the  thickness  of 
the  film.  Films  of  sulphate  of  lime,  the  0-00124  and 
0-01818  of  an  inch  respectively,  give  white  light  in  what- 
ever position  they  may  be  held,  provided  they  be  per- 
pendicular to  the  polarized  ray ;  but  films  of  interme- 
diate thickness  will  give  all  colors.  Consequently,  a 
wedge  of  sulphate  of  lime,  varying  in  thickness  between 
the  0-00124  and  the  0-01818  of  an  inch,  will  appear  to 
be  striped  with  all  colors  when  polarized  light  is  trans- 
mitted through  it.  A  change  in  the  inclination  of  the 
film,  whether  of  mica  or  sulphate  of  lime,  is  evidently 
equivalent  to  a  variation  in  thickness. 

When  a  plate  of  mica,  held  as  close  to  the  eyes  as 
possible  at  such  an  inclination  as  to  transmit  the  polar- 
ized ray  along  one  of  its  optic  axes,  is  viewed  through  the 
tourmaline  with,  its  axis  vertical,  a  most  splendid  appear- 

Q 


182  COLORED  IMAGES.  SECT.  XXII. 

ance  is  presented.  The  cloudy  spot  in  the  direction  of 
the  optic  axis  is  seen  surrounded  by  a  set  of  vividly 
colored  rings  of  an  oval  form,  divided  into  two  unequal 
parts  by  a  black  curved  band  passing  through  the  cloudy 
spot  about  which  the  rings  are  formed.  The  other  optic 
axis  of  the  mica  exhibits  a  similar  image  (N.  207). 

When  the  two  optic  axes  of  a  crystal  make  a  small 
angle  with  one  another,  as  in  nitre,  the  two  sets  of  rings 
touch  externally ;  and  if  the  plate  of  nitre  be  turned  round 
in  its  own  plane,  the  black  transverse  bands  undergo 
a  variety  of  changes,  till  at  last  the  whole  richly  colored 
image  assumes  the  form  of  the  figure  8,  traversed  by  a 
black  cross  (N.  208).  Substances  with  one  optic  axis 
have  but  one  set  of  colored  circular  rings,  with  a  broad 
black  cross  passing  through  its  center,  dividing  the  rings 
into  four  equal  parts.  When  the  analyzing  plate  re- 
volves, this  figure  recurs  at  eveiy  quarter  revolution ; 
but  in  the  intermediate  positions  it  assumes  the  com- 
plementary colors,  the  black  cross  becoming  white. 

It  is  in  vain  to  attempt  to  describe  the  beautiful  phe- 
nomena exhibited  by  innumerable  bodies,  which  undergo 
periodic  changes  in  form  and  color  when  the  analyzing 
plate  revolves,  but  not  one  of  them  shows  a  trace  of 
color  without  the  aid  of  tourmaline  or  something  equiv- 
alent to  analyze  the  light,  and  as  it  were  to  call  these 
beautiful  phantoms  into  existence.  Tourmaline  has  the 
disadvantage  of  being  itself  a  colored  substance  ;  but 
that  inconvenience  may  be  obviated  by  employing  a  re- 
flecting surface  as  an  analyzing  plate.  When  polarized 
light  is  reflected  by  a  plate  of  glass  at  the  polarizing 
angle,  it  will  be  separated  into  two  colored  pencils;  and 
when  the  analyzing  plate  is  turned  round  in  its  own 
plane,  it  will  alternately  reflect  each  ray  at  every  quar- 
ter revolution,  so  that  all  the  phenomena  that  have  been 
described  will  be  seen  by  reflection  on  its  surface. 

Colored  rings  are  produced  by  analyzing  polarized 
light  transmitted  through  glass  melted  and  suddenly  or 
unequally  cooled ;  also  through  thin  plates  of  glass 
bent  with  the  hand,  jelly  indurated  or  compressed,  &c. 
&c.  In  short,  all  the  phenomena  of  colored  rings  may 
be  produced,  either  permanently  or  transiently,  in  a 
variety  of  substances,  by  heat  and  cold,  rapid  cooling, 


SICT.  xxn.         cmcuLAR  POLARIZATION.  183 

compression,  dilatation,  and  induration ;  and  so  little 
apparatus  is  necessary  for  performing  the  experiments, 
that,  as  Sir  John  Herschel  says,  a  piece  of  window- 
glass  or  a  polished  table  to  polarize  the  light,  a  sheet  of 
clear  ice  to  produce  the  rings,  and  a  broken  fragment 
of  plate -glass  placed  near  the  eye  to  analyze  the  light, 
are  alone  requisite  to  produce  one  of  the  most  splendid 
of  optical  exhibitions. 

It  has  been  observed,  that  when  a  ray  of  light, 
polarized  by  reflection  from  any  surface  not  metallic,  is 
analyzed  by  a  doubly  refracting  substance,  it  exhibits 
properties  wfiich  are  symmetrical  both  to  the  right  and 
left  of  the  plane  of  reflection,  and  the  ray  is  then  said 
to  be  polarized  according  to  that  plane.  This  symmetry 
is  not  destroyed  when  the  ray,  before  being  analyzed, 
traverses  the  optic  axis  of  a  crystal  having  but  one 
optic  axis,  as  evidently  appears  from  the  circular  forms 
of  the  colored  rings  already  described.  Regularly  crys- 
talized  quartz,  however,  forms  an  exception.  ID  it, 
even  though  the  rays  should  pass  through  the  optic 
axis  itself,  where  there  is  no  double  refraction,  the 
primitive  symmetry  of  the  ray  is  destroyed,  and  the 
plane  of  primitive  polarization  deviates  either  to  the 
right  or  left  of  the  observer,  by  an  angle  proportional 
to  the  thickness  of  the  plate  of  quartz.  This  angular 
motion,  or  true  rotation  of  the  plane  of  polarization, 
which  is  called  circular  polarization,  is  clearly  proved  by 
the  phenomena.  The  colored  rings  produced  by  all 
crystals  having  but  one  optic  axis  are  circular,  and 
traversed  by  a  black  cross  concentric  with  the  rings ;  so 
that  the  light  entirely  vanishes  throughout  the  space 
inclosed  by  the  interior  ring,  because  there  is  neither 
double  refraction  nor  polarization  along  the  optic  axis. 
But  in  the  system  of  rings  produced  by  a  plate  of 
quartz,  whose  surfaces  are  perpendicular  to  the  axis  of 
the  crystal,  the  part  within  the  interior  ring,  instead  of 
being  void  of  light,  is  occupied  by  a  uniform  tint  of  red, 
green,  or  blue,  according  to  the  thickness  of  the  plate 
(N.  209).  Suppose  the  plate  of  quartz  to  be  ^  of  an 
inch  thick,  which  will  give  the  red  tint  to  th'e  space 
within  the  interior  ring;  when  the  analyzing  plate  is 
turned  in  its  own  plane  through  an  angle  of  17|°,  the 


184  CIRCULAR  POLARIZATION.  SECT.  XXII. 

red  hue  vanishes.  If  a  plate  of  rock  crystal  ^  of  an 
inch  thick  be  used,  the  analyzing  plate  must  revolve 
through  35°  before  the  red  tint  vanishes,  and  so  on ; 
every  additional  25th  of  an  inch  in  thickness  requiring 
an  additional  rotation  of  17^°  ;  whence  it  is  manifest 
that  the  plane  of  polarization  revolves  in  the  direction 
of  a  spiral  within  the  rock  crystal.  It  is  remarkable 
that  in  some  crystals  of  quartz,  the  plane  of  polarization 
revolves  from  right  to  left,  and  in  others  from  left  to 
right,  although  the  crystals  themselves  differ  apparently 
only  by  a  very  slight,  almost  imperceptible  variety  in 
form.  In  these  phenomena,  the  rotation  to  the  right  is 
accomplished  according  to  the  same  laws,  and  with  the 
same  energy,  as  that  to  the  left.  But  if  two  plates  of 
quartz  be  interposed  which  possess  different  affections, 
the  second  plate  undoes,  either  wholly  or  partly,  the 
rotatory  motion  which  the  first  had  produced,  according 
as  the  plates  are  of  equal  or  unequal  thickness.  When 
the  plates  are  of  unequal  thickness,  the  deviation  is  in 
the  direction  of  the  strongest,  and  exactly  the  same 
with  that  which  a  third  plate  would  produce  equal  in 
thickness  to  the  difference  of  the  two. 

M.  Biot  has  discovered  the  same  properties  in  a 
variety  of  liquids.  Oil  of  turpentine,  and  an  essential 
oil  of  laurel,  cause  the  plane  of  polarization  to  turn  to 
the  left,  whereas  the  syrup  of  sugar-cane,  and  a  solu- 
tion of  natural  camphor  by  alcohol,  turn  it  to  the  right. 
A  compensation  is  effected  by  the  superposition  or 
mixture  of  two  liquids  which  possess  these  opposite 
properties,  provided  no  chemical  action  takes  place.  A 
remarkable  difference  was  also  observed  by  M.  Biot 
between  the  action  of  the  particles  of  the  same  sub- 
stances when  in  a  liquid  or  solid  state.  The  syrup  of 
grapes,  for  example,  turns  the  plane  of  polarization  to 
the  left  as  long  as  it  remains  liquid ;  but  as  soon  as  it 
acquires  the  solid  form  of  sugar,  it  causes  the  plane  of 
polarization  to  revolve  toward  the  right,  a  property 
which  it  retains  even  when  again  dissolved.  Instances 
occur  also  in  which  these  circumstances  are  reversed. 

A  ray  of  light  passing  through  a  liquid  possessing  the 
power  of  circular  polarization  is  not  affected  by  mixing 
other  fluids  with  the  liquid— such  as  water,  ether,  alco- 


SECT.  XXII.  CIRCULAR  POLARIZATION.  185 

hol,  &c — which  do  not  possess  circular  polarization 
themselves,  the  angle  of  deviation  remaining  exactly  the 
same  as  before  the  mixture.  Whence  M.  Biot  infers 
that  the  action  exercised  by  the  liquids  in  question 
does  not  depend  upon  their  mass,  but  that  it  is  a  mole- 
cular action  exercised  by  the  ultimate  particles  of  mat- 
ter, which  depends  solely  upon  the  individual  constitu- 
tion, and  is  entirely  independent  of  the  positions  and 
mutual  distances  of  the  particles  with  regard  to  each 
other.  These  important  discoveries  show,  that  circular 
polarization  surpasses  the  power  of  chemical  analysis  hi 
giving  certain  and  direct  evidence  of  the  similarity  or 
difference  existing  in  the  molecular  constitution  of  bodies, 
as  well  as  of  the  permanency  of  that  constitution,  or  of 
the  fluctuations  to  which  it  may  be  liable.  For  example, 
no  chemical  difference  has  been  discovered  between 
syrup  from  the  sugar-cane  and  syrup  from  grapes.  Yet 
the  first  causes  the  plane  of  polarization  to  revolve  to 
the  right,  and  the  other  to  the  left ;  therefore  some  es- 
sential difference  must  exist  in  the  nature  of  then-  ulti- 
mate molecules.  The  same  difference  is  to  be  traced 
between  the  juices  of  such  plants  as  give  sugar  similar 
to  that  from  the  cane,  and  those  which  give  sugar  like 
that  obtained  from  grapes.  This  eminent  philosopher 
is  now  engaged  in  a  series  of  experiments  on  the  pro- 
gressive changes  in  the  sap  of  vegetables  at  different 
distances  from  their  roots,  and  on  the  products  that  are 
formed  at  the  various  epochs  of  vegetation,  from  their 
action  on  polarized  light. 

It  is  a  fact  established  by  M.  Biot,  that  in  circular 
polarization,  the  laws  of  rotation  followed  by  the  differ- 
ent simple  rays  of  light  are  dissimilar  in  different  sub- 
stances. Whence  he  infers  that  the  deviation  of  the 
simple  rays  from  one  another  ought  not  to  result  from 
a  special  property  of  the  luminous  principle  only,  but 
that  the  proper  action  of  the  molecules  must  also  concur 
in  modifying  the  deviations  of  the  simple  rays  differently 
in  different  substances. 

One  of  the  many  brilliant  discoveries  of  M.  Fresne 
is  the  production  of  circular  and  elliptical  polarization  by 
the  internal  reflection  of  light  from  plate  glass.  He  has 
shown  that  if  light  polarized  by  any  of  the  usual  methods 


186  ELLIPTICAL  POLARIZATION.  SECT.  XXII. 

be  twice  reflected  within  a  glass  rhomb  (N.  1 G6)  of  a  given 
form,  the  vibrations  of  the  ether  that  are  perpendicular 
to  the  plane  of  incidence  will  be  retarded  a  quarter  of  a 
vibration,  which  causes  the  vibrating  particles  to  describe 
circles,  and  the  succession  of  such  vibrating  particles 
throughout  the  extent  of  a  wave  to  form  altogether  a 
circular  helix,  or  curve  like  a  corkscrew.  However, 
that  only  happens  when  the  plane  of  polarization  is 
inclined  at  an  angle  of  45°  to  the  plane  of  incidence. 
When  these  two  planes  form  an  angle  either  greater 
or  less,  the  succession  of  vibrating  particles  forms  an 
elliptical  helix,  which  curve  may  be  represented  by 
twisting  a  thread  in  a  spiral  about  an  oval  rod.  These 
curves  will  turn  to  the  right  or  left,  according  to  the 
position  of  the  incident  plane. 

The  motion  of  the  ethereal  medium  in  elliptical  and 
circular  polarization  may  be  represented  by  the  analogy 
of  a  stretched  cord  ;  for  if  the  extremity  of  such  a  cord 
be  agitated  at  equal  and  regular  intervals  by  a  vibratory 
motion  entirely  confined  to  one  plane,  the  cord  will  be 
thrown  into  an  undulating  curve  lying  wholly  in  that 
plane.  If  to  this  motion  there  be  superadded  another 
similar  and  equal,  but  perpendicular  to  the  first,  the 
cord  will  assume  the  form  of  an  elliptical  helix ;  its  ex- 
tremity will  describe  an  ellipse,  and  every  molecule 
throughout  its  length  will  successively  do  the  same.  But 
if  the  second  system  of  vibrations  commence  exactly  a 
quarter  of  an  undulation  later  than  the  first,  the  cord  will 
take  the  form  of  a  circular  helix  or  cork-screw ;  the 
extremity  will  move  uniformly  in  a  circle,  and  every 
molecule  throughout  the  cord  will  do  the  same  in  suc- 
cession. It  appears,  therefore,  that  both  circular  and 
elliptical  polarization  may  be  produced,  by  the  compo- 
sition of  the  motions  of  two  rays  in  which  the  particles 
cf  ether  vibrate  in  places  at  right  angles  to  one  another. 

Professor  Airy,  in  a  very  profound  and  able  paper 
published  in  the  Cambridge  Transactions,  has  proved 
that  all  the  different  kinds  of  polarized  light  are  obtained 
from  rock  crystal.  When  polarized  light  is  transmitted 
through  the  axis  of  a  crystal  of  quartz,  in  the  emergent 
ray  the  particles  of  ether  move  in  a  circular  helix;  and 
when  it  is  transmitted  obliquely  so  as  to  form  an  angle 


SECT.  XXII.          ELLIPTICAL  POLARIZATION.  187 

with  the  axis  of  the  prism,  the  particles  of  ether  move 
in  an  elliptical  helix,  the  ellipticity  increasing  with  the 
obliquity  of  the  incident  ray ;  so  that,  when  the  incident 
ray  falls  perpendicularly  to  the  axis,  the  particles  of 
ether  move  in  a  straight  line.  Thus  quartz  exhibits 
every  variety  of  elliptical  polarization,  even  including 
the  extreme  cases  where  the  eccentricity  is  zero,  or 
equal  to  the  greater  axis  of  the  ellipse  (N.  210).  In 
many  crystals  the  two  rays  are  so  little  separated,  that 
it  is  only  from  the  nature  of  the  transmitted  light  that 
they  are  known  to  have  the  property  of  double  refrac- 
tion. M.  Fresnel  discovered  by  experiments  on  the 
properties  of  light  passing  through  the  axis  of  quartz, 
that  it  consists  of  two  superposed  rays,  moving  with 
different  velocities ;  and  Professor  Airy  has  shown,  that 
in  these  two  rays,  the  molecules  of  ether  vibrate  in 
similar  ellipses  at  right  angles  to  each  other,  but  in  dif- 
ferent directions ;  that  their  ellipticity  varies  with  the 
angle  which  the  incident  ray  makes  with  the  axis ;  and 
that,  by  the  composition  of  their  motions,  they  produce 
all  the  phenomena  of  polarized  light  observed  in  quartz. 

It  appears  from  what  has  been  said,  that  the  mole- 
cules of  ether  always  perform  their  vibrations  at  right 
angles  to  the  direction  of  the  ray,  but  very  differently  in 
the  various  kinds  of  light.  In  natural  light  the  vibrations 
are  rectilinear,  and  in  every  plane.  In  ordinary  polar- 
ized light  they  are  rectilinear,  but  confined  to  one  plane  ; 
in  circular  polarization  the  vibrations  are  circular ;  and 
in  elliptical  polarization  the  molecules  vibrate  in  ellipses. 
These  vibrations  are  communicated  from  molecule  to 
molecule,  in  straight  lines  when  they  are  rectilinear,  in 
a  circular  helix  when  they  are  circular,  and  in  an  oval 
or  elliptical  helix  when  elliptical. 

Some  fluids  possess  the  property  of  circular  polar- 
ization, as  oil  of  turpentine ;  and  elliptical  polarization, 
or  something  similar,  seems  to  be  produced  by  reflection 
from  metallic  surfaces. 

The  colored  images  from  polarized  light  arise  from 
the  interference  of  the  rays  (N.  211).  MM.  Fresnel 
and  Arago  found  that  two  rays  of  polarized  light  inter- 
fere and  produce  colored  fringes  if  they  be  polarized  in 
the  same  plane,  but  that  they  do  not  interfere  when 


188  FORMATION  OF  IMAGES.  SECT.  XXII. 

polarized  in  different  planes.  In  all  intermediate  posi- 
tions, fringes  of  intermediate  brightness  are  produced. 
The  analogy  of  a  stretched  cord  will  show  how  this 
happens.  Suppose  the  cord  to  be  moved  backward  and 
forward  horizontally  at  equal  intervals ;  it  will  be  thrown 
into  an  undulating  curve  lying  all  in  one  plane.  If  to 
this  motion  there  be  superadded  another  similar  and 
equal,  commencing  exactly  half  an  undulation  later  than 
the  first,  it  is  evident  that  the  direct  motion  every  mole- 
cule will  assume,  in  consequence  of  the  first  system  of 
waves,  will  at  every  instant  be  exactly  neutralized  by 
the  retrograde  motion  it  would  take  in  virtue  of  the 
second ;  and  the  cord  itself  will  be  quiescent  in  conse- 
quence of  the  interference.  But  if  the  second  system 
of  waves  be  in  a  plane  perpendicular  to  the  first,  the 
effect  would  only  be  to  twist  the  rope,  so  that  no  inter- 
ference would  take  place.  Rays  polarized  at  right  an- 
gles to  each  other  may  subsequently  be  brought  into  the 
same  plane  without  acquiring  the  property  of  producing 
colored  fringes  ;  but  if  they  belong  to  a  pencil  the  whole 
of  which  was  originally  polarized  in  the  same  plane,  they 
will  interfere. 

The  manner  in  which  the  colored  images  are  formed 
may  be  conceived,  by  considering  that  when  polarized 
light  passes  through  the  optic  axis  of  a  doubly  refracting 
substance, — as  mica,  for  example, — it  is  divided  into  two 
pencils  by  the  analyzing  tourmaline ;  and  as  one  ray  is 
absorbed  there  can  be  no  interference.  But  when 
polarized  light  passes  through  the  mica  in  any  other 
direction,  it  is  separated  into  two  white  rays,  and  these 
are  again  divided  into  four  pencils  by  the  tourmaline, 
which  absorbs  two  of  them ;  and  the  other  two,  being 
transmitted  in  the  same  plane  with  different  velocities, 
interfere  and  produce  the  colored  phenomena.  If  the 
analysis  be  made  with  Iceland  spar,  the  single  ray  pass- 
ing through  the  optic  axis  of  the  mica  will  be  refracted 
into  two  rays  polarized  in  different  planes,  and  no  in- 
terference will  happen.  But  when  two  rays  are  trans- 
mitted by  the  mica,  they  will  be  separated  into  four  by 
the  spar,  two  of  which  will  interfere  to  form  one  image, 
and  the  other  two,  by  their  interference,  will  produce 
the  complementary  colors  of  the  other  image,  when  the 


SKCT.  XXII.        DISCOVERY  OF  POLARIZATION.  189 

spar  has  revolved  through  90° ;  because,  in  such  posi- 
tions of  the  spar  as  produce  the  colored  images,  only 
two  rays  are  visible  at  a  time,  the  other  two  being  re- 
flected. When  the  analysis  is  accomplished  by  reflec- 
tion, if  two  rays  are  transmitted  by  the  mica,  they  are 
polarized  in  planes  at  right  angles  to  each  other.  And 
if  the  plane  of  reflection  of  either  of  these  rays  be  at 
right  angles  to  the  plane  of  polarization,  only  one  of 
them  will  be  reflected,  and  therefore  no  interference 
can  take  place ;  but  in  all  other  positions  of  the  analy- 
zing plate  both  rays  will  be  reflected  in  the  same  plane, 
and  consequently  will  produce  colored  rings  by  their 
interference. 

It  is  evident  that  a  great  deal  of  the  light  we  see  must 
be  polarized,  since  most  bodies  which  have  the  power 
of  reflecting  or  refracting  light  also  have  the  power  of 
polarizing  it.  The  blue  light  of  the  sky  is  completely 
polarized  at  an  angle  of  74°  from  the  sun  in  a  plane 
passing  through  his  center. 

A  constellation  of  talent  almost  unrivaled  at  any 
period  in  the  history  of  science,  has  contributed  to  the 
theory  of  polarization,  though  the  original  discovery  of 
that  property  of  light  was  accidental,  and  arose  from  an 
occurrence  which  like  thousands  of  others  would  have 
passed  unnoticed,  had  it  not  happened  to  one  of  those 
rare  minds  capable  of  drawing  the  most  important  in- 
ferences from  circumstances  apparently  trifling.  In 
1808,  while  M.  Malus  was  accidently  viewing  with  a 
doubly-refracting  prism  a  brilliant  sunset  reflected  from 
the  windows  of  the  Luxembourg  palace  in  Paris,  on 
turning  the  prism  slowly  round,  he  was  surprised  to 
see  a  very  great  difference  in  the  intensity  of  the  two 
images,  die  most  refracted  alternately  changing  from 
brightness  to  obscurity  at  each  quadrant  of  revolution. 
A  phenomenon  so  unlocked  for  induced  him  to  investi- 
gate its  cause,  whence  sprung  one  of  the  most  elegant 
and  refined  branches  of  physical  optics. 


190  OBJECTIONS  REMOVED.  SEC*.  XXIII. 


SECTION  XXIII. 

Objections  to  the  Undulatory  Theory,  from  a  Difference  iu  the  Action  of 
Sound  and  Light  under  the  same  circumstances,  removed — The  Disper- 
sion of  Light  according  to  the  Undulatory  Theory. 

THE  numerous  phenomena  of  periodical  colors  arising 
from  the  interference  of  light,  which  do  not  admit  of 
satisfactory  explanation  on  any  other  principle  than  the 
undulatory  theory,  are  the  strongest  arguments  in  favor 
of  that  hypothesis ;  and  even  cases  which  at  one  time 
seemed  unfavorable  to  that  doctrine  have  proved  upon 
investigation  to  proceed  from  it  alone.  Such  is  the  er- 
roneous objection  which  has  been  made,  in  consequence 
of  a  difference  in  the  mode  of  action  of  light  and  sound, 
under  the  same  circumstances,  in  one  particular  in- 
stance. When  a  ray  of  light  from  a  luminous  point, 
and  a  diverging  sound,  are  both  transmitted  through  a 
very  small  hole  into  a  dark  room,  the  light  goes  straight 
forward  and  illuminates  a  small  spot  on  the  opposite  wall, 
leaving  the  rest  in  darkness ;  whereas  the  sound  on  en- 
tering diverges  in  all  directions,  and  is  heard  in  every 
part  of  the  room.  These  phenomena,  however,  instead 
of  being  at  variance  with  the  undulatory  theoiy,  are 
direct  consequences  of  it,  arising  from  the  very  great 
difference  between  the  magnitude  of  the  undulations  of 
sound  and  those  of  light.  The  undulations  of  light  are 
incomparably  less  than  the  minute  aperture,  while  those 
of  sound  are  much  greater.  Therefore  when  light  di- 
verging from  a  luminous  point  enters  the  hole,  the  rays 
round  its  edges  are  oblique,  and  consequently  of  different 
lengths,  while  those  in  the  center  are  direct,  and  nearly 
or  altogether  of  the  same  lengths.  So  that  the  small 
undulations  between  the  center  and  the  edges  are  in 
different  phases,  that  is,  in  different  states  of  undula- 
tion. Therefore  the  greater  number  of  them  interfere, 
and  by  destroying  one  another  produce  darkness  all 
around  the  edges  of  the  aperture  ;  whereas  the  central 
rays  having  the  same  phases,  combine,  and  produce  a 
spot  of  bright  light  on  a  wall  or  screen  directly  opposite 
the  hole.  The  waves  of  air  producing  sound,  on  the 


SECT.  XX1JI.  OBJECTIONS  REMOVED.  191 

contrary,  being  very  large  compared  with  the  hole,  da 
not  sensibly  diverge  hi  passing  through  it.  and  are  there- 
fore all  so  nearly  of  the  same  length,  and  consequently 
in  the  same  phase,  or  state  of  undulation,  that  none  of 
them  interfere  sufficiently  to  destroy  one  another. 
Hence  all  the  particles  of  air  in  the  room  are  set  into  a 
state  of  vibration,  so  that  the  intensity  of  the  sound  is 
very  nearly  everywhere  the  same.  Strong  as  the  pre- 
ceding cases  may  be,  the  following  experiment  made  by 
M.  Arago  about  twenty  years  ago  seems  to  be  decisive 
in  favor  of  the  undulatory  doctrine.  Suppose  a  plano- 
convex lens  of  very  great  radius  to  be  placed  upon  a 
plate  of  very  highly  polished  metal.  When  a  ray  of 
polarized  light  falls  upon  this  apparatus  at  a  very  great 
angle  of  incidence,  Newton's  rings  are  seen  at  the  point 
of  contact.  But  as  the  polarizing  angle  of  glass  differs 
from  that  of  metal,  when  the  light  falls  on  the  lens  at 
the  polarizing  angle  of  glass,  the  black  spot  and  the  sys- 
tem of  rings  vanish.  For  although  light  in  abundance 
continues  to  be  reflected  from  the  surface  of  the  metal, 
not  a  ray  is  reflected  from  the  surface  of  the  glass  that 
is  in  contact  with  it,  consequently  no  interference  can 
take  place ;  which  proves,  beyond  a  doubt,  that  New- 
ton's rings  result  from  the  interference  of  the  light  re- 
flected from  both  the  surfaces  apparently  in  contact  (N. 
194). 

Notwithstanding  the  successful  adaptation  of  the  un- 
dulatory system  to  phenomena,  the  dispersion  of  light 
for  a  long  time  offered  a  formidable  objection  to  that    , 
theory,  which  has  only  been  removed  during  the  present 
year  by  Professor  Powell  of  Oxford. 

A  sunbeam  falling  on  a  prism,  instead  of  being  re- 
fracted to  a  single  point  of  white  light,  is  separated  into 
its  component  colors,  which  are  dispersed  or  scattered 
unequally  over  a  considerable  space,  of  which  the  portion 
occupied  by  the  red  rays  is  the  least,  and  that  over  which 
the  violet  rays  are  dispersed  is  the  greatest.  Thus  the 
rays  of  the  colored  spectrum  whose  waves  are  of  differ- 
ent lengths,  have  different  degrees  of  refrangibility,  and 
consequently  move  with  different  velocities,  either  in  the 
medium  which  conveys  the  light  from  the  sun,  or  in  the 
refracting  medium,  or  in  both ;  whereas  rays  of  all  colors 


192  OBJECTIONS  REMOVED.  SECT.  XXIII. 

come  from  the  sun  to  the  earth  with  the  same  velocity. 
If,  indeed,  the  velocities  of  the  various  rays  were  differ- 
ent in  space,  the  aberration  of  the  fixed  stars,  which  is 
inversely  as  the  velocity,  would  be  different  for  different 
colors,  and  every  star  would  appear  as  a  spectrum  whose 
length  would  be  parallel  to  the  direction  of  the  earth's 
motion,  which  is  not  found  to  agree  with  observation. 
Besides,  there  is  no  such  difference  in  the  velocities  of 
the  long  and  short  waves  of  air  in  the  analogous  case  of 
sound,  since  notes  of  the  lowest  and  highest  pitch  are 
heard  in  the  order  in  which  they  are  struck.  In  fact, 
when  the  sunbeam  passes  from  air  into  the  prism  its 
velocity  is  diminished  ;  and  as  its  refraction  and  conse- 
quently its  dispersion  depend  solely  upon  the  diminished 
velocity  of  the  transmission  of  its  waves,  they  ought  to 
be  the  same  for  waves  of  all  lengths,  unless  a  connection 
exists  between  the  length  of  a  wave,  and  the  velocity 
with  which  it  is  propagated.  Now  this  connection  be- 
tween the  length  of  a  wave  of  any  color  and  its  velocity 
or  refrangibility  in  a  given  medium,  has  been  deduced 
by  Professor  Powell  from  M.  Cauchy's  investigations  of 
the  properties  of  light  on  a  peculiar  modification  of  the 
undulatory  hypothesis.  Hence  the  refrangibility  of  the 
various  colored  rays  computed  from  this  relation  for  any 
given  medium,  when  compared  with  their  refrangibility 
in  the  same  medium  determined  by  actual  observation, 
will  show  whether  the  dispersion  of  light  comes  under 
the  laws  of  that  theory.  But  in  order  to  accomplish 
this,  it  is  clear  that  the  length  of  the  waves  should  be 
found  independently  of  refraction,  and  a  very  beautiful 
discoveiy  of  M.  Fraunhofer  furnishes  the  means  of 
doing  so. 

That  philosopher  obtained  a  perfectly  pure  and  com- 
plete colored  spectrum  with  all  its  dark  and  bright  lines 
by  the  interference  of  light  alone,  from  a  sunbeam  pass- 
ing through  a  series  of  fine  parallel  wires  covering  the 
object  glass  of  a  telescope.  In  this  spectrum,  formed 
independently  of  prismatic  refraction,  the  positions  of 
the  colored  rays  depend  only  on  the  lengths  of  their 
waves,  and  M.  Fraunhofer  found  that  the  intervals  be- 
tween them  are  precisely  proportional  to  the  differences 
of  these  lengths.  He  measured  the  lengths  of  the  waves 


SICT.  XXIV.  OBJECTIONS  REMOVED.  193 

of  the  different  colors  at  seven  fixed  points,  determined 
by  seven  of  the  principal  dark  and  bright  lines.  Profes- 
sor Powell,  availing  himself  of  these  measures,  has  made 
the  requisite  computations,  and  has  found  that  the  coin- 
cidence of  theory  with  observation  is  perfect  for  ten 
substances  whose  refrangibility  had  been  previously  de- 
termined by  the  direct  measurements  of  M.  Fraunhofer, 
and  for  ten  others  whose  refrangibility  has  more  recently 
been  ascertained  by  M.  Rudberg,  Thus,  in  the  case  of 
seven  rays  in  each  of  twenty  different  substances  solid 
and  fluid,  the  dispersion  of  light  takes  place  according  to 
the  laws  of  the  undulatory  theoiy;  and  as  there  can 
hardly  be  a  doubt  that  dispersion  hi  all  other  bodies  will 
be  found  to  follow  the  same  law,  the  undulatory  theory 
of  light  may  now  be  regarded  as  completely  established. 
It  is  however  an  express  condition  of  the  connection  be- 
tween the  velocity  of  light  and  the  length  of  its  undula- 
tions, that  the  intervals  between  the  vibrating  molecules 
of  the  ethereal  fluid  should  bear  a  sensible  relation  to 
the  length  of  an  undulation.  The  coincidence  of  the 
computed  with  the  observed  refractions  shows  that  this 
condition  is  fulfilled  within  the  refracting  media ;  but 
the  aberration  of  the  fixed  stars  leads  to  the  inference 
that  it  does  not  hold  in  the  ethereal  regions,  where  the 
velocities  of  the  rays  of  all  colors  are  the  same. 


SECTION  XXIV. 

Chemical  or  Photographic  Rays  of  the  Solar  Spectrum — Messrs.  Scheele, 
Ritter,  and  Wollaston's  Discoveries — Mr.  Wedgewood  and  Sir  Humphry 
Davy's  Photographic  Pictures — The  Calotype — The  Daguerreotype — 
The  Chromatype — The  Cyanotype — Sir  John  Herschel's  Discoveries  in 
the  Photographic  or  Chemical  Spectrum — Mons.  E.  Becquerel's  Discovery 
of  Inactive  Lines  in  the  Chemical  Spectrum. 

THE  solar  spectrum  has  assumed  a  totally  new  char- 
acter from  recent  analysis,  especially  the  chemical  por- 
tion, which  exercises  an  energetic  action  on  matter,  pro- 
ducing the  most  wonderful  and  mysterious  changes  on 
the  organized  and  unorganized  creation. 

All  bodies  are  probably  affected  by  light,  but  it  acts 
with  greatest  energy  on  such  as  are  of  weak  chemical 
affinity,  imparting  properties  to  them  which  they  did 
13  R 


194  THE  CALOTYPE.  SECT.  XXIV. 

not  possess  before.  Metallic  salts,  especially  those  of 
silver,  whose  molecules  are  held  together  by  an  unstable 
equilibrium,  are  of  all  bodies  the  most  susceptible  of  its 
influence  ;  the  effects  however  vary  with  the  substances 
employed  and  with  the  different  rays  of  the  solar  spec- 
trum, the  chemical  properties  of  which  are  by  no  means 
alike.  As  early  as  1772  M.  Scheele  showed  that  the 
pure  white  color  of  chloride  of  silver  was  rapidly  dark- 
ened by  the  blue  rays  of  the  solar  spectrum,  while  the 
red  rays  had  no  effect  upon  it;  and  in  1801  M.  Hitter 
discovered  that  invisible  rays  beyond  the  violet  extremity 
have  the  property  of  blackening  argentine  salts,  that 
this  property  diminishes  toward  the  less  refrangible  part 
of  the  spectrum,  and  that  the  red  rays  have  an  opposite 
quality,  that  of  restoring  the  blackened  saltaflfLsilver  to 
its  original  purity,  from  which  he  inferredB3gthe  most 
refrangible  extremity  of  the  spectrum  ha^pn  oxygen- 
izing power,  and  the  other  that  of  deoxygenating.  Dr. 
Wollaston  found  that  gum  guaiacum  acquires  a  green 
color  in  the  violet  and  blue  rays,  and  resumes  its  original 

fin  the  red.  No  attempt  had  been  made  to  trace 
ural  objects  by  means  of  light  reflected  from  them 
Mr.  Wedgewood,  together  with  Sir  Humphry  Davy, 
took  up  the  subject:  they  produced  profiles  and  tracings 
of  objects  on  surfaces  prepared  with  nitrate  and  chloride 
of  silver,  but  they  did  not  succeed  in  rendering  their 
pictures  permanent.  This  difficulty  was  overcome  in 
1814  by  M.  Niepce,  who  produced  a  permanent  picture 
of  surrounding  objects,  by  placing  in  the  focus  of  a 
camera  obscura,  a  metallic  plate  covered  with  a  film  of 
asphalt  dissolved  in  oil  of  lavender. 

MA  Fox  Talbot,  without  any  knowledge  of  M.  Niepce's 
experiments,  had  been  engaged  in  the  same  pursuit, 
and  -must  be  regarded  as  an  independent  inventor  of 
photography,  one  of  the  most  beautiful  arts  of  modern 
times :  he  was  the  first  who  succeeded  in  using  paper 
chemically  prepared  for  receiving  impressions  from  nat- 
ural objects ;  and  he  also  discovered  a  method  of  fixing 
permanently  the  impressions — that  is,  of  rendering  the 
paper  insensible  to  any  further  action  of  light.  In  the 
calotypo,  one  of  Mr.  Talbot's  most  recent  applications 
of  the  art,  this  photographic  surface  is  prepared  by  wash- 


S«CT.  XXIV.  M.  DAGUERRE  195 

ing  smooth  writing-ffoper,  first  with  a  solution  of  nitrate 
of  silver,  then  with  bromide  of  potassium,  and  again  with 
nitrate  of  silver,  drying  it  at  a  fire  after  each  washing ; 
the  paper  is  thus  rendered  so  sensitive  to  light  that  even 
the  passage  of  a  thin  cloud  is  perceptible  on  it,  conse- 
quently it  must  be  prepared  by  candle-light.  Portraits, 
buildings,  insects,  leaves  of  plants,  in  short  every  object 
is  accurately  delineated  in  a  few  seconds,  and  in  the 
focus  of  a  camera  obscura  the  most  minute  objects  are 
so  exactly  depicted  that  the  microscope  reveals  new 
beauties. 

Since  the  effect  of  the  chemical  agency  of  light  is  to 
destroy  the  affinity  between  the  salt  and  the  silver,  Mr. 
Talbot  found  that  in  order  to  render  these  impressions 
permanent^pn  paper,  it  was  only  necessary  to  wash  it 
with  saJBB  water,  or  with  a  solution  of  iodide  of  po- 
tassiunaf^Wr  these  liquids  the  liquid  hyposulphites 
have  been*  advantageously  substituted,  which  are  the 
most  efficacious  in  dissolving  and  removing  the  unchanged 
salt,  leaving  the  reduced  silver  on  the  paper.  The  cal- 
otype  picture  is  negative,  that  is,  the  lights  and  shadows 
are  the  reverse  of  what  they  are  in  nature,  and  «{& 
right-hand  side  in  nature  is  the  left  in  the  picture ;  but 
if  it  be  placed  with  its  face  pressed  against  photographic 
paper,  between  a  board  and  a  plate  of  glass,  and  exposed 
to  the  sun  a  short  time,  a  positive  and  direct  picture  as 
it  is  in  nature  is  formed ;  engravings  may  be  exactly 
copied  by  this  simple  process,  and  a  direct  picture  may 
be  produced  at  once  by  using  photographic  paper  already 
made  brown  by  exposure  to  light. 

While  Mr.  Fox  Talbot  was  engaged  in  these  very 
elegant  discoveries  in  England,  M.  Daguerre  had  brought 
to  perfection  and  made  public  that  admirable  process  by 
which  he  has  compelled  Nature  permanently  to  en- 
grave her  own  works ;  and  thus  the  talents  of  France 
and  England  have  been  combined  in  bringing  to  perfec- 
tion this  useful  art.  Copper,  plated  with  silver,  is  suc- 
cessfully employed  by  M.  Daguerre  for  copying  nature 
by  the  agency  of  light.  The  surface  of  the  plate  is 
converted  into  an  iodide  of  silver,  by  placing  it  horizon- 
tally with  its  face  downward  in  a  covered  box,  in  the 
bottom  of  which  there  is  a,  small  quantity  of  iodine 


196  THE  CHROMATYPE.  S«cr.  XXiV. 

which  evaporates  spontaneously.  In  three  or  four 
minutes  the  surface  acquires  a  yellow  tint,  and  then, 
screening  it  carefully  from  light,  it  must  be  placed  in 
the  focus  of  a  camera  obscura,  where  an  invisible  image 
of  external  objects  will  be  impressed  on  it  in  a  few 
minutes.  When  taken  out  the  plate  must  be  exposed 
in  another  box  to  the  action  of  mercurial  vapor,  which 
attaches  itself  to  those  parts  of  the  plate  which  had 
been  exposed  to  light,  but  does  not  adhere  to  such  parts 
as  had  been  in  shadow  ;  and  as  the  quantity  of  mercury 
over  the  other  parts  is  in  exact  proportion  to  the  de- 
gree of  illumination,  the  shading  of  the  picture  is  per- 
fect. The  image  is  fixed,  first  by  removing  the  iodine 
from  the  plate,  by  plunging  it  into  hyposulphite  of  soda, 
and  then  washing  it  in  distilled  water  ;  by  this  process 
the  yellow  color  is  destroyed,  and  in  order  to  render 
the  mercury  permanent,  the  plate  must  be  exposed  a 
few  minutes  to  nitric  vapor,  then  placed  in  nitric  acid 
containing  copper  or  silver  in  solution  at  a  temperature 
of  61|°  of  Fahrenheit  for  a  short  time,  and  lastly 
polished  with  chalk.  This  final  part  of  the  process  is 
due  to  Dr.  Berre,  of  Vienna. 

Nothing  can  be  more  beautiful  than  the  shading  of 
these  chiar-oscuro  pictures  when  objects  are  at  rest, 
but  the  least  motion  destroys  the  effect ;  the  method 
therefore  is  more  applicable  to  buildings  than  landscape. 
Color  alone  is  wanting ;  but  the  researches  of  Sir  John 
Herschel  give  reason  to  believe  that  even  this  will  ulti- 
mately be  attained. 

The  most  perfect  impressions  of  seaweeds,  leaves  of 
plants,  feathers,  &c.,  may  be  formed  by  bringing  the 
object  into  close  contact  with  a- sheet  of  photographic 
paper,  between  a  board  and  plate  of  glass  ;  then  ex- 
posing the  whole  to  the  sun  for  a  short  time,  and  after- 
ward fixing  it  by  the  process  described.  The  colors  of 
the  pictures  vary  with  the  preparation  of  the  paper,  by 
which  almost  any  tint  may  be  produced. 

In  the  chromatype,  a  peculiar  photograph  discovered 
by  Mr.  Hunt,  chromate  of  copper  is  used,  on  which  a 
dark  brown  negative  image  is  first  formed,  but  by  the 
continued  action  of  light  it  is  changed  to  a  positive 
yellow  picture  on  a  white  ground ;  the  farther  effect 


S«CT.  XXIV.  DISTRIBUTION  OP  CHEMICAL  ENERGY.  ]  97 

of  light  is  checked  by  washing  the  picture  in  pure 
water. 

In  cyanotypes,  a  class  of  photographs  discovered  by 
Sir  John  Herschel,  in  which  cyanogen  in  its  combina- 
tions with  iron  forms  the  ground,  the  pictures  are 
Prussian  blue  and  white.  In  the  chrysotype  of  the 
same  eminent  philosopher,  the  image  is  first  received 
on  paper  prepared  with  the  ammonia-citrate  of  iron, 
and  afterward  washed  with  a  neutral  solution  of  gold. 
It  is  fixed  by  water  acidulated  with  sulphuric  acid,  and 
lastly  by  hydriodate  of  potash,  from  which  a  white  and 
purple  photograph  results.  It  is  vain  to  attempt  to  de- 
scribe the  various  beautiful  effects  which  Sir  John 
Herschel  obtained  from  chemical  compounds,  and  from 
the  juices  of  plants  :  the  juice  of  the  red  poppy  gives  a 
positive  bluish  purple  image,  that  of  the  ten-week  stock 
a  fine  rose  color  on  a  pale  straw-colored  ground. 

Pictures  may  be  made  by  exposure  to  sunshine,  on 
all  compound  substances  having  a  weak  chemical  affinity, 
but  the  image  is  often  invisible,  as  in  the  Daguerreotype, 
till  brought  out  by  washing  in  some  chemical  prepara- 
tion. Water  is  frequently  sufficient ;  indeed  Sir  John 
Herschel  brought  out  dormant  photographs  by  breathing 
on  them,  and  some  substances  are  insensible  to  the  ac- 
tion of  light  till  moistened,  as  for  example  gum  guaia- 
cum.  Argentine  papers,  however,  are  little  subject  to 
the  influence  of  moisture.  The  power  of  the  solar  rays 
is  augmented  in  certain  cases  by  placing  a  plate  of  glass 
in  close  contact  over  the  sensitive  surface. 

Chemical  action  always  accompanies  the  sun's  light, 
but  the  analysis  of  the  solar  spectrum  has  partly  dis- 
closed the  wonderful  nature  of  the  emanation.  In  the 
research,  properties  most  important  and  unexpected 
have  been  discovered  by  Sir  John  Herschel,  who  im- 
prints the  stamp  of  genius  on  all  he  touches — his  elo- 
quent papers  can  alone  convey  an  adequate  idea  of  then? 
value  in  opening  a  field  of  inquiry  vast  and  untrodden. 
The  following  brief  and  imperfect  account  of  his  exper- 
iments is  all  that  can  be  attempted  here : — 

A  certain  degree  of  chemical  energy  is  distributed 
through  every  part  of  the  solar  spectrum,  and  also  to  a 
considerable  extent  through  the  dark  spaces  at  each  ex- 


198  INTENSITY  OF  CHEMICAL  ACTION.     SECT.  XXIV. 

tremity.  This  distribution  does  not  depend  on  the  re- 
frangibility  of  the  rays  alone,  but  also  on  the  nature  of 
the  rays  themselves,  and  on  the  physical  properties  of 
the  analyzing  medium  on  which  the  rays  are  received, 
whose  changes  indicate  and  measure  their  action.  The 
length  of  the  photographic  image  of  the  same  solar  spec- 
trum varies  with  the  physical  qualities  of  the  surface  on 
which  it  is  impressed.  When  the  solar  spectrum  is 
received  on  paper  prepared  with  bromide  of  silver,  the 
chemical  spectrum,  as  indicated  merely  by  the  length  of 
the  darkened  part,  includes  within  its  limits  the  whole 
luminous  spectrum,  extending  in  one  direction  far  be- 
yond the  extreme  violet  and  lavender  rays,  and  in  the 
other  down  to  the  extremest  red :  with  tartrate  of  sil- 
ver the  darkening  occupies  not  only  all  the  space  under 
the  most  refrangible  rays,  but  reaches  much  beyond  the 
extreme  red.  On  paper  prepared  with  formobenzoate 
of  silver  the  chemical  spectrum  is  cut  off  at  the  orange 
rays,  with  phosphate  of  silver  in  the  yellow,  and  with 
chloride  of  gold  it  terminates  with  the  green,  with  car- 
bonate of  mercury  it  ends  in  the  blue,  and  on  paper 
prepared  with  the  per  cyanide  of  gold,  ammonia,  and 
nitrate  of  silver,  the  darkening  lies  entirely  beyond  the 
visible  spectrum  at  its  most  refrangible  extremity,  and 
is  only  half  its  length,  whereas  in  some  cases  chemical 
action  occupies  a  space  more  than  twice  the  length  of 
the  luminous  image. 

The  point  of  maximum  energy  of  chemical  action 
varies  as  much  for  different  preparations  as  the  scale  of 
action.  In  the  greater  number  of  cases  the  point  of 
deepest  blackening  lies  about  the  lower  edge  of  the  in- 
digo rays,  though  in  no  two  cases  is  it  exactly  the  same, 
and  in  many  substances  it  is  widely  different.  On  paper 
prepared  with  the  juice  of  the  ten-week  stock  (Mathiola 
annua),  there  are  two  maxima,  one  in  the  mean  yellow 
and  a  weaker  in  the  violet ;  and  on  a  preparation  of  tar- 
trate of  silver,  Sir  John  Herschel  found  three,  one  in 
the  least  refrangible  blue,  one  in  the  indigo,  and  a  third 
beyond  the  visible  violet.  The  decrease  in  photographic 
energy  is  seldom  perfectly  alike  on  both  sides  of  the 
maximum.  Thus  at  the  most  refrangible  end  of  the 
solar  spectrum  the  greatest  chemical  power  is  exerted 


SBCT.  XXIV.  THE  SOLAR  SPECTRUM.  199 

in  most  instances  where  there  fa  least  light  and  heat, 
and  even  in  the  space  where  both  sensibly  cease. 

Not  only  the  intensity  but  the  kind  of  action  is  differ- 
ent in  the  different  points  of  the  solar  spectrum,  as 
evidently  appears  from  the  various  colors  that  are  fre- 
quently  impressed  on  the  same  analyzing  surface,  each 
ray  having  a  tendency  to  impart  its  own  color.  Sir  John 
Herschel  obtained  a  colored  image  of  the  solar  spectrum 
on  paper  prepared  according  to  Mr.  Talbot's  principle, 
from  a  sunbeam  refracted  by  a  glass  prism  and  then 
highly  condensed  by  a  lens.  The  photographic  image 
was  rapidly  formed  and  very  intense,  and  when  with- 
drawn from  the  spectrum  and  viewed  in  common  day- 
light it  was  found  to  be  colored  with  sombre  but  une- 
quivocal tints  imitating  the  prismatic  colors,  which  varied 
gradually  from  red  through  green  and  blue^to  a  purplish 
black.  After  washing  the  surface  in  water,  the  tints 
became  more  decided  by  being  kept  a  few  days  in  the 
dark — a  phenomenon,  Sir  John  observes,  of  constant 
occurrence,  whatever  be  the  preparation  of  the  paper, 
provided  colors  are  produced  at  all.  He  also  obtained  a 
colored  image  on  nitrate  of  silver,  the  part  under  the 
blue  rays  becoming  a  blue  brown,  while  that  under  the 
violet  had  a  pinkish  shade,  and  sometimes  green  ap- 
peared at  the  point  corresponding  to  the  least  refrangible 
blue.  Mr.  Hunt  found  on  a  paper  prepared  with  fluoride 
of  silver  that  a  yellow  line  was  impressed  on  the  space 
occupied  by  the  yellow  rays,  a  green  band  on  the  space 
under  the  green  rays,  an  intense  blue  throughout  the 
space  on  which  the  blue  and  indigo  rays  fell,  and  under 
the  violet  rays  a  ruddy  brown  appeared  ;  these  colors 
remained  clear  and  distinct  after  being  kept  two  months. 

Notwithstanding  the  great  variety  in  the  scale  of 
action  of  the  solar  spectrum,  the  darkening  or  deoxy- 
dizing  principle  that  prevails  in  the  more  refrangible 
part  rarely  surpasses  or  even  attains  the  mean  yellow 
ray  which  is  the  point  of  maximum  illumination ;  it  is 
generally  cut  off  abruptly  at  that  point  which  seems  to 
form  a  limit  between  the  opposing  powers  which  prevail 
at  the  two  ends  of  the  spectrum.  The  bleaching  or  ox- 
ydizing  effect  of  the  red  rays  on  blacke'ned  muriate  of 
silver  discovered  by  M.  Ritter  of  Jena,  and  the  resfora- 


200  CHEMICAL  SPECTRUM.  SECT.  XXIV. 

tion  by  the  same  rays  of  discolored  gum  guaiacum  to  its 
original  tint  by  Dr.  YVollaston,  have  already  been  men- 
tioned as  giving  the  first  indications  of  that  difference  in 
the  mode  of  action  of  the  chemical  rays  at  the  two  ends 
of  the  visible  spectrum,  now  placed  beyond  a  doubt. 

The  action  exerted  by  the  less  refrangible  rays  be- 
yond and  at  the  red  extremity  of  the  solar  spectrum,  in 
most  instances,  so  far  from  blackening  metallic  salts, 
protects  them  from  the  action  of  the  diffused  daylight; 
but  if  the  prepared  surface  has  already  been  blackened 
by  exposure  to  the  sun,  they  possess  the  remarkable 
property  of  bleaching  it  in  some  cases,  and  under  other 
circumstances  of  changing  the  black  surface  into  a  fiery 
red. 

Sir  John  Herschel,  to  whom  we  owe  most  of  our 
knowledge  of  the  properties  of  the  chemical  spectrum, 
prepared  a  sheet  of  paper  by  washing  it  with  muriate 
of  ammonia,  and  then  with  two  coats  of  nitrate  of  silver ; 
on  this  surface  he  obtained  an  impression  of  the  solar 
spectrum  exhibiting  a  range  of  colors  very  nearly  cor- 
responding with  its  natural  hues.  But  a  very  remarka- 
ble phenomenon  occurred  at  the  end  of  least  refrangi- 
bility ;  the  red  rays  exerted  a  protecting  influence 
which  preserved  the  paper  from  the  change  which  it 
would  otherwise  have  undergone  from  the  deoxydizing 
influence  of  the  dispersed  light  which  always  surrounds 
the  solar  spectrum,  and  this  maintained  its  whiteness. 
Sir  John  met  with  another  instance  on  paper  prepared 
with  bromide  of  silver,  on  which  the  whole  of  the  space 
occupied  by  the  visible  spectrum  was  darkened  down  to 
the  very  extremity  of  the  red  rays,  but  an  oxydizing 
action  commenced  beyond  the  extreme  red,  which  main- 
tained the  whiteness  of  the  paper  to  a  considerable  dis- 
tance beyond  the  last  traceable  limit  of  the  visible  rays, 
thus  evincing  decidedly  the  existence  of  some  chemical 
power  over  a  considerable  space  beyond  the  least  re- 
frangible end  of  the  spectrum.  Mr.  Hunt  also  found 
that  on  the  Daguerreotype  plate  a  powerful  protecting 
influence  is  exercised  by  the  extreme  red  rays.  In 
these  cases  the  red  and  those  dark  rays  beyond  them 
exert  an  action -of  an  opposite  nature  to  that  of  the  violet 
and  lavender  ravs. 


Sicr.XXIV.   BLEACHING  POWER  OF  SOLAR  SPECTRUM.    201 

The  least  refrangible  part  of  the  solar  spectrum  pos- 
sesses also,  under  certain  circumstances,  a  bleaching 
property,  by  which  the  metallic  salts  are  restored  to 
their  original  whiteness  after  being  blackened  by  ex- 
posure to  common  daylight,  or  to  the  most  refrangible 
rays  of  the  solar  spectrum. 

Paper  prepared  with  iodide  of  silver,  when  washed 
over  with  ferrocyanite  of  potash,  blackens  Vapidly  when 
exposed  to  the  solar  spectrum.  It  begins  in  the  violet 
rays  and  extends  over  all  the  space  occupied  by  the  dark 
chemical  rays,  and  over  the  whole  visible  spectrum 
down  to  the  extreme  red  rays.  This  image  is  colored, 
the  red  rays  giving  a  reddish  tint  and  the  blue  a  bluish. 
In  a  short  time  a  bleaching  process  begins  under  the  red 
rays,  and  extends  upward  to  the  green,  but  the  space 
occupied  by  the  extreme  red  is  maintained  perfectly  dark. 
Mr.  Hunt  found  that  a  similar  bleaching  power  is  exerted 
by  the  red  rays  on  paper  prepared  with  protocyanide  of 
potassium  and  gold  with  a  wash  of  nitrate  of  silver. 

The  application  of  a  moderately  strong  hydriodate  of 
potash  to  darkened  photographic  paper  renders  it  pecu- 
liarly susceptible  of  "being  whitened  by  further  exposure 
to  light.  If  paper  prepared  with  bromide  of  silver  be 
washed  with  ferrocyanate  of  potash  while  under  the 
influence  of  the  solar  spectrum,  it  is  immediately  dark- 
ened throughout  the  part  exposed  to  the  visible  rays 
down  to  the  end  of  the  red,  some  slight  interference 
being  perceptible  about  the  region  of  the  orange  and 
yellow.  After  this  a  bleaching  action  begins  over  the 
part  occupied  by  the  red  rays,  which  extends  to  the 
green.  By  longer  exposure  an  oval  spot  begins  again  to 
darken  about  the  center  of  the  bleached  space ;  but  if 
the  paper  receive  another  wash  of  the  hydriodate  of 
potash,  the  bleaching  action  extends  up  from  the  green, 
over  the  region  occupied  by  the  most  refrangible  rays 
and  considerably  beyond  them,  thus  inducing  a  negative 
action  in  the  most  refrangible  part  of  the  spectrum. 

In  certain  circumstances  the  red  rays,  instead  of  re- 
storing darkened  photographic  paper  to  its  original 
whiteness,  produce  a  deep  red  color.  When  Sir  John 
Herschel  received  the  spectrum  on  paper  somewhat 
discolored  by  exposure  to  direct  sunshine,  instead  of 


202  PHOTOGRAPHY.  SECT.  XXIV. 

whiteness,  a  red  border  was  formed  extending  from  the 
space  occupied  by  the  orange,  and  nearly  covering  that 
on  which  the  red  fell.  When,  instead  of  exposing  the 
paper  in  the  first  instance  to  direct  sunshine,  it  was 
blackened  by  the  violet  rays  of  a  prismatic  spectrum,  or 
by  a  sunbeam  that  had  undergone  the  absorptive  action 
of  a  solution  of  ammonia-sulphate  of  copper,  the  red 
rays  of  the  condensed  spectrum  produced  on  it,  not 
whiteness,  but  a  full  and  fiery  red  which  occupied  the 
whole  space  on  which  any  of  the  visible  red  rays  had 
fallen,  and  this  red  remained  unchanged,  however  long 
the  paper  remained  exposed  to  the  least  refrangible  rays. 

Sunlight  transmitted  through  red  glass  produces  the 
same  effect  as  the  red  rays  of  the  spectrum  in  the  fore- 
going experiment.  Sir  John  Herschel  placed  an  en- 
graving over  a  paper  blackened  by  exposure  to  sunshine, 
covering  the  whole  with  a  dark  red-brown  glass  previ- 
ously ascertained  to  absorb  every  ray  beyond  the  orange : 
in  this  way  a  photographic  copy  was  obtained  in  which 
the  shades  were  black,  as  in  the  original  engraving,  but 
the  lights,  instead  of  being  white,  were  of  the  red  color 
of  venous  blood,  and  no  other  color  could  be  obtained  by 
exposure  to  light,  however  long.  Sir  John  ascertained 
that  every  part  of  the  spectrum  impressed  by  the  more 
refrangible  rays  is  equally  reddened,  or  nearly  so,  by  the 
subsequent  action  of  the  less  refrangible ;  thus  the  red 
rays  have  the  very  remarkable  property  of  assimilating 
to  their  own  color  the  blackness  already  impressed  on 
photographic  paper. 

That  there  is  a  deoxy dating  property  in  the  more  re- 
frangible rays,  and  an  oxydating  action  in  the  less  re- 
frangible part  of  the  spectrum,  is  manifest  from  the 
blackening  of  one  and  the  bleaching  effect  of  the  other ; 
but  the  peculiar  action  of  the  red  rays  in  the  experi- 
ments mentioned,  shows  that  some  other  principle  exists 
different  from  contrariety  of  action.  These  opposite 
qualities  are  balanced  or  neutralized  in  the  region  of  the 
mean  yellow  ray.  But  although  this  is  the  general 
character  of  the  photographic  spectrum,  under  certain 
circumstances  even  the  red  rays  have  a  deoxydating 
power,  while  the  blue  and  scarlet  exert  a  contrary  influ- 
ence ;  but  these  are  rare  exceptions.  - 


S.CT.  XXIV.  REFRANGIBILITY.  203 

The  photographic  action  of  the  two  portions  of  the 
solar  spectrum  being  so  different,  Sir  John  Herschel 
tried  the  effect  of  their  united  action  by  superposing  the 
less  refrangible  part  of  the  spectrum  over  the  more  re- 
frangible portion  by  means  of  two  prisms,  and  he  thus 
discovered  that  two  rays  of  different  refrangibility,  and 
therefore  of  different  lengths  of  undulation,  acting  simul- 
taneously, produce  an  effect  which  neither  acting  sepa- 
rately can  do. 

Some  circumstances  that  occurred  during  the  analysis 
of  the  chemical  spectrum  seem  to  indicate  an  absorptive 
action  in  the  sun's  atmosphere.  The  spectral  image 
impressed  on  paper  prepared  with  nitrate  of  silver  and 
Rochelle  salt,  commenced  at  or  very  little  below  the 
mean  yellow  ray,  of  a  delicate  lead  color,  and  when  tha 
action  was  arrested  such  was  the  character  of  the  whole 
photographic  spectrum.  But  when  the  light  of  the 
solar  spectrum  was  allowed  to  continue  its  action,  there 
was  observed  to  come  on  suddenly  a  new  and  much 
more  intense  impression  of  darkness,  confined  in  length 
to  the  blue  and  violet  rays ;  and  what  is  most  remarka- 
ble, confined  also  in  breadth  to  the  middle  of  the  sun's 
image,  so  far  at  least  as  to  leave  a  border  of  the  lead- 
colored  spectrum  traceable,  not  only  round  the  clear 
and  well-defined  convexity  of  the  dark  interior  spectrum 
at  the  least  refrangible  end,  but  also  laterally  along  both 
its  edges :  and  this  border  was  the  more  easily  traced 
and  less  liable  to  be  mistaken  from  its  striking  contrast 
of  color  with  the  interior  spectrum,  the  former  being 
lead  gray,  the  latter  an  extremely  rich  deep  velvety 
brown.  The  less  refrangible  end  of  this  interior  brown 
spectrum  presented  a  sharply  terminated  and  regularly 
elliptical  contour,  the  more  refrangible  a  less  decided 
one.  "  It  may  seem  too  hazardous,"  Sir  John  continues, 
"  $o  look  for  the  cause  of  this  very  singular  phenomenon 
in  a  real  difference  between  the  chemical  agencies  of 
those  rays  which  issue  from  the  central  portion  of  the 
sun's  disc,  and  those  which,  emanating  from  its  borders, 
have  undergone  the  absorptive  action  of  a  much  greater 
depth  of  its  atmosphere  ;  and  yet  I  confess  myself  some- 
what at  a  loss  what  other  cause  to  assign  for  it.  It 
must  suffice,  however,  to  have  thrown  out  the  hint,  re- 


204  PHOTOGRAPHIC  PHENOMENA.         SKCT.  XXIV. 

marking  only,  that  I  have  other,  and  I  am  disposed  to 
think  decisive,  evidence  of  the  existence  of  an  absorptive 
solar  atmosphere  extending  beyond  the  luminous  one." 
Several  circumstances  concur  in  showing  that  there  are 
influences  also  concerned  in  the  transmission  of  the  pho- 
tographic action  which  have  not  yet  been  explained,  as 
for  example  the  influence  which  the  time  of  the  day 
exercises  on  the  rapidity  with  which  photographic  im- 
pressions are  made,  the  sun  being  much  less  effective 
two  hours  after  passing  the  meridian  than  two  hours 
before.  There  is  also  reason  to  Nsuspect  that  the  effect 
in  some  way  depends  on  the  latitude,  since  a  much 
longer  time  is  required  to  obtain  an  image  under  the 
bright  skies  of  the  tropics  than  in  England,  and  it  is 
even  probable  that  there  is  a  difference  in  the  sun's 
light  in  high  and  low  latitudes,  because  an  image  of  the 
solar  spectrum  obtained  on  a  Daguerreotype  plate  in 
Virginia  by  Dr.- Draper,  differed  from  a  spectral  image 
obtained  by  Mr.  Hunt  on  a  similar  plate  in  England. 
The  inactive  spaces  discovered  in  the  photographic  spec- 
trum by  M.  E.  Becquerel  similar  to  those  in  the  lumi- 
nous spectrum,  and  coinciding  with  them,  is  also  a  phe- 
nomenon of  which  no  explanation  has  yet  been  given. 
Although  chemical  action  extends  over  the  whole  lumi- 
nous spectrum  and  much  beyond  it  in  gradations  of 
more  or  less  intensity,  it  is  found  by  careful  investiga- 
tion to  be  by  no  means  continuous  ;  numerous  inactive 
lines  cross  it  coinciding  with  those  in  the  luminous  image 
as  far  as  it  extends :  besides,  a  very  great  number  exist 
in  the  portions  that  are  obscure,  and  which  overlap  the 
visible  part.  There  are  three  extra-spectral  lines  be- 
yond the  red,  and  some  strongly  marked  groups  on  the 
obscure  part  beyond  the  violet ;  but  the  whole  number 
of  those  inactive  lines,  especially  in  the  dark  spaces,  is 
so  great  that  it  is  impossible  to  count  them. 

Notwithstanding  this  coincidence  in  the  inactive  lines 
of  the  two  spectra,  photographic  energy  is  independent 
of  both  light  and  heat,  since  it  exerts  the  most  powerful 
influence  in  those  rays  where  they  are  least,  and  also 
in  spaces  where  neither  sensibly  exist ;  but  the  trans- 
mission of  the  sun's  light  through  colored  media  makes 
that  independence  quite  evident.  Heat  and  light  pass 


SKUT.  XXIV.         PHOTOGRAPHIC  PHENOMENA.  ',205 

abundantly  through  yellow  glass,  or  a  solution  of  chro- 
mate  of  potash  ;  but  the  greater  part  of  the  chemical 
rays  are  excluded,  and  chlorine  gas  diluted  with  common 
air,  though  highly  pervious  to  the  luminous  and  calorific 
principles,  has  the  same  effect.  Sir  John  Herschel 
found  that  a  slight  degree  of  yellow  London  fog  had  a 
similar  effect  with  that  of  pale  yellow  media :  he  also 
remarked  that  a  weak  solution  of  azolitmine  in  potash, 
which  admits  a  great  quantity  of  green  light,  excludes 
chemical  action  ;  and  some  years  ago,  the  author,  while 
making  experiments  on  the  transmission  of  chemical 
rays,  observed  that  green  glass,  colored  byoxyde  of  cop- 
per, about- the  20th  of  an  inck  thick,  excludes  the  pho- 
tographic rays,  and  as  M.  Melloni  has  shown  that  sub- 
stance to  be  impervious  to  the  most  refrangible  calorific 
rays,  it  has  the  property  of  excluding  the  whole  of  the 
most  refrangible  part  of  the  solar  spectrum,  visible  and 
invisible.  Green  mica,  if  not  too  thin,  has  also  the  same 
effect,  whereas  amethyst,  deep  blue  and  violet-colored 
glasses,  though  they  transmit  a  very  little  light,  allow 
the  chemical  rays  to  pass  freely.  Thus  light  and  pho- 
tographic energy  may  be  regarded  as  distinct  and  inde- 
pendent properties  of  the  solar  beam. 

It  is  not  known  whether  photographic  energy  be  ab- 
sorbed by  material  substances  or  not,  neither  is  it  known 
whether  it  be  concerned  in  crystalization,  and  in  pro- 
ducing those  changes  in  the  internal  structure  of  cfystals 
when  exposed  to  the  sun,  already  mentioned  ;  but  the 
power  is  universal  wherever  the  solar  beam  falls,  though 
the  effect  only  becomes  evident  in  cases  of  unstable  mo- 
lecular equilibrium.  The  composition  and  decomposi- 
tion of  those  solids,  liquids,  and  ae'riform  fluids  hitherto 
attributed  to  light,  are  chiefly  owing  to  this  energy  ;  and 
as  similar  chemical  changes  may  be  produced  by  cur- 
rents of  electricity,  an  occult  connection  between  these 
two  imponderable  influences  is  shadowed  out, 
8 


206  HEAT  SECT.  XXV. 


SECTION  XXV. 

Heat — Calorific  Rays  of  the  Solar  Spectrum — Experiments  of  MM.  De 
Laroche  and  Melloni  on  the  Transmission  of  Heat — The  Point  of  greatest 
Heat  in  the  Solar  Spectrum  varies  with  the  Substance  of  the  Prism — 
Polarization  of  Heat— Circular  Polarization  of  Heat — Transmission  of  the 
Chemical  Rays — Absorption  of  Heat — Radiation  of  Heat — Dew — Hoar 
Frost — Rain — Hail — Combustion — Dilatation  of  Bodies  by  Heat— Propa- 
gation of  Heat — Latent  Heat — Heat  presumed  to  consist  of  the  Undula- 
tions of  an  Elastic  Medium — Parathermic  Rays — Moser's  Discoveries. 

IT  is  not  by  vision  alone  that  a  knowledge  of  the  sun's 
rays  is  acquired,  —  touch  proves  that  they  have  the 
power  of  raising  the  temperature  of  substances  exposed 
to  their  action.  Sir  William  Herschel  discovered  that 
rays  of  caloric  which  produce  the  sensation  of  heat,  exist 
in  the  solar  spectrum  independently  of  those  of  light ; 
when  he  used  a  prism  of  flint-glass,  he  found  the  warm 
rays  most  abundant  in  the  dark  space  a  little  beyond  the 
red  extremity  of  the  spectrum — that  from  thence  they 
decrease  toward  the  violet,  beyond  which  they  are  in- 
sensible. It  may  therefore  be  concluded,  that  the  ca- 
lorific rays  vary  in  refrangibility,  and  that  those  beyond 
the  extreme  red  are  less  refrangible  than  any  rays  of 
light.  Since  Sir  William  Herschel's  time  it  has  been 
discovered  that  the  calorific  spectrum  exceeds  the  lumi- 
nous one  in  length  in  the  ratio  of  42  to  25,  but  the  most 
singular  phenomenon  of  the  calorific  spectrum  is  its 
want  of  continuity.  Sir  John  Herschel  blackened  the 
under  side  of  a  sheet  of  very  thin  white  paper  by  the 
smoke  of  a  lamp,  and  having  exposed  the  white  side  to 
the  solar  spectrum,  he  drew  a  brush  dipped  in  spirit  of 
whie  over  it,  by  which  the  paper  assumed  a  black  hue 
when  sufficiently  saturated.  The  heat  in  the  spectrum 
evaporated  tha  spirit  first  on  those  parts  of  the  paper 
where  it  fell  with  greatest  intensity,  thereby  restoring 
their  white  color,  and  thus  he  discovered  that  the  ca- 
loric is  not  distributed  uniformly,  but  in  spots  of  greater 
or  less  intensity — a  circumstance  probably  owing  to  the 
absorbing  action  of  the  atmospheres  of  the  sun  and 
earth.  "  The  effect  of  the  former,"  says  Sir  John,  u  is 
beyond  our  control,  unless  we  could  carry  our  experi- 
ments to  such  a  point  of  delicacy  as  to  operate  separately 


SKCT.  XXV.  SOLAR  SPECTRUM.  207 

on  rays  emanating  from  the  center  and  borders  of  the 
sun's  disc ;  that  of  the  earth's,  though  it  cannot  be  elim- 
inated any  more  than  in  the  case  of  the  sun's,  may  yet 
be  varied  to  a  considerable  extent  by  experiments  made 
at  great  elevations  and  under  a  vertical  sun,  and  com- 
pared with  others  where  the  sun  is  more  oblique,  the 
situation  lower,  and  the  atmospheric  pressure  of  a  tem- 
porarily high  amount.  Should  it  be  found  that  this 
cause  is  in  reality  concerned  in  the  production  of  the 
spots,  we  should  see  reason  to  believe  that  a  large  por- 
tion of  solar  heat  never  reaches  the  earth's  surface,  and 
that  what  is  incident  on  the  summits  of  lofty  mountains 
differs  not  only  in  quantity,  but  also  in  quality,  from 
what  the  plains  receive." 

Thus  the  solar  spectrum  is  proved  to  consist  of  five 
superposed  spectra,  only  three  of  which  are  visible — 
the  red,  yellow,  and  blue;  each  of  the  five  varies  in 
refrangibility  and  intensity  throughout  the  whole  ex- 
tent, the  visible  part  being  overlapped  at  one  extremity 
by  the  chemical,  and  at  the  other  by  the  calorific  rays ; 
but  the  two  latter  exceed  the  visible  part  so  much,  that 
the  linear  dimensions  of  the  three,  the  luminous,  calo- 
rific, and  photographic,  are  in  the  proportion  of  the 
numbers  25,  42,  10,  and  55-10,  so  that  the  whole  solar 
spectrum  is  more  than  twice  as  long  as  its  visible  part. 

That  the  heat-producing  rays  exist  independently  of 
light,  is  a  matter  of  constant  experience  in  the  abundant 
emission  of  them  from  boiling  water.  Yet  there  is 
every  reason  to  believe  that  both  the  calorific  and 
chemical  rays  are  modifications  of  the  same  agent 
which  produces  the  sensation  of  light.  Rays  of  heat 
dart  in  diverging  straight  lines  from  flame,  and  from 
each  point  in  the  surfaces  of  hot  bodies,  in  the  same 
manner  as  diverging  rays  of  light  proceed  from  every 
point  of  the  surfaces  of  such  as  are  luminous.  Accord- 
ing to  the  experiments  of  Sir  John  Leslie,  radiation 
proceeds  not  only  from  the  surfaces  of  substances,  but 
also  from  the  particles  at  a  minute  depth  below  it.  He 
found  that  the  emission  is  most  abundant  in  a  direction 
perpendicular  to  the  radiating  surface,  and  that  it  is 
more  rapid  from  a  rough  than  from  a  polished  surface  : 
radiation,  however,  can  only  take  place  in  air  and  in 


208  RADIATION.  SECT.  XXV. 

vacuo ;  it  is  altogether  imperceptible  when  the  hot 
body  is  inclosed  in  a  solid  or  liquid.  Heated  substances, 
when  exposed  to  the  open  air,  continue  to  radiate 
caloric  till  they  become  nearly  of  the  temperature  of 
the  surrounding  medium.  The  radiation  is  very  rapid 
at  first,  but  diminishes  according  to  a  known  law  with 
the  temperature  of  the  heated  body.  It  appears,  also, 
that  the  radiating  power  of  a  surface  is  inversely  as  its 
reflecting  power ;  and  bodies  that  are  most  impermea- 
ble to  heat  radiate  least. 

Rays  of  heat,  whether  they  proceed  from  the  sun, 
from  flame,  or  other  terrestrial  sources,  luminous  or 
non-luminous,  are  instantaneously  transmitted  through 
solid  and  liquid  substances,  there  being  no  appreciable 
difference  in  the  time  they  take  to  pass  through  layers 
of  any  nature  or  thickness  whatever.  They  pass  also 
with  the  same  facility  whether  the  media  be  agitated 
or  at  rest;  and  in  these  respects  the  analogy  between 
light  and  heat  is  perfect.  Radiant  heat  passes  through 
the  gases  with  the  same  facility  as  light ;  but  a  remark- 
able difference  obtains  in  the  transmission  of  light  and 
heat  through  most  solid  and  liquid  substances,  the  same 
body  being  often  perfectly  permeable  to  the  luminous 
and  altogether  impermeable  to  the  calorific  rays.  For 
example,  thin  and  perfectly  transparent  plates  of  alum 
and  citric  acid  sensibly  transmit  all  the  rays  of  light 
from  an  argand  lamp,  but  stop  eight  or  nine  tenths  of 
the  concomitant  heat ;  while  a  large  piece  of  brown 
rock  crystal  gives  a  free  passage  to  the  radiant  heat, 
but  intercepts  almost  all  the  light.  M.  Melloni  has 
established  the  general  law  in  uncrystalized  substances 
such  as  glass  and  liquids,  that  the  property  of  instanta- 
neously transmitting  heat  is  in  proportion  to  their  re- 
fractive powers.  The  law,  however,  is  entirely  at  fault 
in  bodies  of  a  crystaline  texture.  Carbonate  of  lead, 
for  instance,  which  is  colorless,  and  possesses  a  very 
high  refractive  power  with  regard  to  light,  transmits 
less  radiant  heat  than  Iceland  spar  or  rock-crystal, 
which  are  very  inferior  to  it  in  the  order  of  refran- 
gibility ;  while  rock-salt,  which  has  the  same  transpa- 
rency and  refractive  power  with  alum  and  citric  acid, 
transmits  six  or  eight  times  as  much  caloric.  This 


SICT.  XXV.  TRANSMISSION  OP  HEAT.  209 

remarkable  difference  in  the  transmissive  power  of  sub- 
stances having  the  same-  appearance,  is  attributed  by  M. 
Melloni  to  their  crystaline  form,  and  hot  to  the  chemical 
composition  of  their  molecules,  as  the  following  experi- 
ments prove.     A  block  of  common  salt  cut  into  plates, 
entirely  excludes  calorific  radiation ;  yet  when  dissolved 
in  water,  it  increases  the  transmissive  power  of  that 
liquid :  moreover,  the  transmissive  power  of  water  is 
increased  in  nearly  the  same  degree,  whether  salt  or 
alum    be    dissolved   in   k ;    yet   these  two    substances 
transmit  very  different  quantities  of  heat  in  their  solid 
state.     Notwithstanding  the  influence  of  ciy stall zation 
on  the  transmissive  power  of  bodies,  no  relation  has 
been  traced  between  that  power  and  the  crystaline  form. 
The  transmission  of  radiant  heat  is  analogous  to  that 
of  light  through  colored  media.     When  common  white 
light,  consisting  of  blue,  yellow,  and  red  rays,  passes 
through  a  red  liquid,  almost  all  the  blue  and  yellow  rays, 
and  a  few  of  the  red,  are  intercepted  by  the  first  layer 
of  the  fluid ;  fewer  are  intercepted  by  the  second, 
less  by  the  third,  and  so  on  :  till  at  last  the  losses  ' 
very  small   and   invariable,  and   those   rays 
transmitted  which  give  the  red  color  to  t1 
a  similar  manner,  when  plates  of  the  sair» 
any  substance,  such  as  glass,  are  exposet 
lamp,  a  considerable  portion  of  the  rad 
rested  by  the  first  plate,  a  less  port^- 
still  less  by  the  third,  and  so  on,  ' ' 
heat  decreasing  till  at  last  the  loss^ 
quantity.     The  traowmssion 
solid  mass  follows  t  '•  @g  ffie 
considerable  on  first 
ish  in  proportion  as 
become  constant  at  a  certain 
difference    between   the   transm> 
through  a  solid  mass,  or  through  the 
cut  into  plates  of  equal  thickness,  arises  . 
quantity  of  heat  that  is  reflected  at  the  surface 
plates.     It  is   evident,  therefore,  that  the  heat 
ually  lost  is  not  intercepted  at  the  surface,  but  ab 
in  the  interior  of  the  substance,  and  that  heat 
has  passed  through  one  stratum  of  air  experiences 
14  s2 


210  RADIANT  HEAT.  SECT.  XXV. 

absorption  in  each  of  the  succeeding  strata,  and  may 
therefore  be  propagated  to  a  greater  distance  before  it 
is  extinguished.  The  experiments  of  M.  de  Laroche 
show,  that  glass,  however  thin,  totally  intercepts  the 
obscure  rays  of  caloric  when  they  flow  from  a  body 
whose  temperature  is  lower  than  that  of  boiling  water ; 
that  as  the  temperature  increases,  the  calorific  rays  are 
transmitted  more  and  more  abundantly ;  and  when  the 
body  becomes  highly  luminous,  that  they  penetrate  the 
glass  with  perfect  ease.  The  extreme  brilliancy  of  the 
sun  is  probably  the  reason  why  his  heat,  when  brought  to 
a  focus  by  a  lens,  is  more  intense  than  any  that  has  been 
produced  artificially.  It  is  owing  to  the  same  cause 
that  glass  screens,  which  entirely  exclude  the  heat  of  a 
common  fire,  are  permeable  by  the  solar  caloric. 

The  results  obtained  by  M.  de  Laroche  have  been 

confirmed  by  the  recent  experiments  of  M.  Melloni  on 

caloric  radiated  from  sources  of  different  temperatures, 

whence  it  appears  that  the  calorific  rays  pass  less  abun- 

*iy  not  only  through  glass,  but  through  rock-crystal, 

spar,  and   other  diaphanous  bodies,   both  solid 

according  as  the  temperature  of  their  origin 

and  that  they  are  altogether  intercepted 

)erature  is  about  that  of  boiling  water. 

as  proved  that  the  heat  emanating  from 

i  a  bright  flame  consists  of  rays  which 

other  as  much  as  the  red,  yellow,  and 

°,h  constitute  white  light.     This  ex- 

vf  the  loss  of  heat  as  it  penetrates 

H  solid   mass,  or  in    passing 

for,  of  the  different  kinds  of 

all  are  successively 

.re  of  the  substance 

till  those  homogeneous  rays 

ve  the  greatest  facility  in  passing 

aeuiar  substance ;  exactly  as  in  a  red 

and  yellow  rays  are  extinguished,  and 

are  transmitted. 

Melloni  employed  four  sources  of  caloric,  two  of 
were  luminous  and  two  obscure ;  namely,  an  oil- 
without  u  glass,  incandescent  platina,  copper 
to  696°,  and  a  copper  vessel  filled  with  water  at 


S«CT.XXV.  MELLONI'S  EXPERIMENTS.  211 

the  temperature  of  178^°  of  Fahrenheit.  Rock-salt 
transmitted  heat  in  the  proportion  of  92  rays  out  of 
100  from  each  of  these  sources;  but  all  other  sub- 
stances pervious  to  radiant  heat,  whether  solid  or 
liquid,  transmitted  more  caloric  from  sources  of  high 
temperature  than  from  such  as  are  low.  For  instance, 
limpid  and  colorless  fluate  of  lime  transmitted  in  the  pro- 
portion of  78  rays  out  of  100  from  the  lamp,  69  from 
the  platiua,  42  from  the  copper,  and  33  from  the  hot 
water;  while  transparent  rock-crystal  transmitted  38 
rays  in  100  from  the  lamp.  28  from  the  platina,  6 
from  the  copper,  and  9  from  the  hot  water.  Pure  ice 
transmitted  only  in  the  proportion  of  6  rays  in  tbte  100 
from  the  lamp,  and  entirely  excluded  those  from  the 
other  three  sources.  Out  of  39  different  substances, 
34  were  pervious  to  the  calorific  rays  from  hot  water, 
14  excluded  those  from  the  hot  copper,  and  4  did  not 
transmit  those  from  the  platina. 

Thus  it  appears  that  heat  proceeding  from  these 
sources  is  of  different  kinds :  this  difference  in 
ture  of  the  calorific  rays  is  also  proved  by  another, 
periment,  which  will  be  more  easily  understood  from 
the  analogy  of  light.  Red  light  emanating  from  red 
glass,  will  pass  in  abundance  through  another  piece  of 
red  glass,  but  it  will  be  absorbed  by  green  glass :  green 
rays  will  more  readily  pass  through  a  green  medium 
than  through  one  of  any  other  color.  This  holds  with 
regard  to  all  colors;  so  in  heat.  Rays  of  caloric  of  the 
same  intensity,  which  have  passed  through  different 
substances,  are  transmitted  in  different  quantities  by  the 
same  piece  of  alum,  and  are  sometimes  stopped  alto- 
gether ;  showing  that  rays  which  emanate  from  different 
substances  possess  different  qualities.  It  appears  that 
a  bright  flame  furnishes  rays  of  heat  of  all  kinds,  in  the 
same  manner  as  it  gives  light  of  all  colors ;  and  as  col- 
ored media  transmit  some  colored  rays  and  absorb  the 
rest,  so  bodies  transmit  some  ray§  of  caloric  and  ex- 
clude the  others.  Rock-salt  alone  resembles  colorless 
transparent  media  in  transmitting  all  kinds  of  caloric, 
even  the  heat  of  the  hand,  just  as  they  transmit  white 
light,  consisting  of  rays  of  all  colors. 

The  property  of  transmitting  the  calorific  rays  di- 


ese  tour 
th«  im- 
:h..-r  ex- 


210  MELLONI'S  EXPERIMENTS.  S£CT.  XXV. 

rainishes  to  a  certain  degree  with  the  thickness  of  the 
body  they  have  to  traverse,  but  not  so  much  as  might 
be  expected.  A  piece  of  veiy  transparent  alum  trans- 
mitted three  or  four  times  less  radiant  heat  from  the 
flame  of  a  lamp  than  a  piece  of  nearly  opaque  quartz 
about  a  hundred  times  as  thick.  However,  the  influ- 
ence of  thickness  upon  the  phenomena  of  transmission 
increases  with  the  decrease  of  temperature  in  the 
origin  of  the  rays,  and  becomes  very  great  when  that 
temperature  is  low.  This  is  a  circumstance  intimately 
connected  with  the  law  established  by  M.  de  Laroche ; 
for  M.  Melloni  observed  that  the  difference  between 
the  quantities  of  caloric  transmitted  by  the  same  plate 
of  glass,  exposed  successively  to  several  sources  of  heat, 
diminished  with  the  thinness  of  the  plate,  and  vanished 
altogether  at  a  certain  limit;  and  that  a  film  of  mica 
transmitted  the  same  quantity  of  caloric,  whether  it 
was  exposed  to  incandescent  platina  or  to  a  mass  of  iron 
heated  to  360°. 

Colored  glasses  transmit  rays  of  light  of  certain 
degrees  of  refrangibility,  and  absorb  those  of  other 
degrees.  For  example,  red  glass  absorbs  the  more 
refrangible  rays,  and  transmits  the  red,  which  are  the 
least  refrangible.  On  the  contrary,  violet  glass  absorbs 
the  least  refrangible,  and  transmits  the  violet,  which 
are  the  most  refrangible.  Now  M.  Melloni  has  found, 
that  although  the  coloring  matter  of  glass  diminishes  its 
power  of  transmitting  heat,  yet  red,  orange,  yellow, 
blue,  violet,  and  white  glass  transmit  calorific  rays  of  all 
degrees  of  refrangibility.  Whereas  green  glass  possesses 
the  peculiar  property  of  transmitting  the  least  refrangi- 
ble calorific  rays,  and  stopping  those  that  are  most  re- 
frangible. It  has  therefore  the  same  elective  action 
for  heat  that  colored  glass  has  for  light,  and  its  action 
on  heat  is  analogous  to  that  of  red  glass  on  light.  Alum 
and  sulphate  of  lime  are  exactly  opposed  to  green  glass 
in  their  action  on  heat,  by  transmitting  the  most  re- 
frangible rays  with  the  greatest  facility. 

The  heat  which  has  already  passed  through  green  or 
opaque  black  glass  will  not  pass  through  alum,  while 
that  which  has  been  transmitted  through ,  glasses  of 
other  colors  traverses  it  readily. 


SKCT.  XXV.  MELLONl'S  EXPERIMENTS.  213 

By  reversing  the  experiment,  and  exposing  different 
substances  to  caloric  that  had  already  passed  through 
alum,  M.  Melloni  found  that  the  heat  emerging  from 
alum  is  almost  totally  intercepted  by  opaque  substances, 
and  is  abundantly  transmitted  by  all  such  as  are  trans- 
parent and  colorless,  and  that  it  suffers  no  appreciable 
loss  when  the  thickness  of  the  plate  is  varied  within 
certain  limits.  The  properties  of  the  heat  therefore 
which  issues  from  alum,  nearly  approach  to  those  of 
light  and  solar  heat. 

Radiant  heat  in  traversing  various  media  is  not  only 
rendered  more  or  less  capable  of  being  transmitted  a 
second  time,  but,  according  to  the  experiments  of  Pro- 
fessor Powell,  it  becomes  more  or  less  susceptible  of 
being  absorbed  in  different  quantities  by  black  orv  white 
surfaces. 

M.  Melloni  has  proved. that  solar  heat  contains  rays 
which  are  affected  by  different  substances  in  the  same 
way  as  if  the  heat  proceeded  from  a  terrestrial  source ; 
whence  he  concludes  that  the  difference  observed  be- 
tween the  transmission  of  terrestrial  and  solar  heat 
arises  from  the  circumstances  of  solar  heat  containing  all 
kinds  of  caloric,  while  in  other  sources  some  of  the  kinds 
are  wanting. 

Radiant  heat,  from  sources  of  any  temperature  what- 
ever, is  subject  to  the  same  laws  of  reflection  and  re- 
fraction as  rays  of  light.  The  index  of  refraction  from 
a  prism  of  rock-salt  determined  experimentally,  is  nearly 
the  same  for  light  and  heat. 

Liquids,  the  various  kinds  of  glass,  and  probably  all 
substances,  whether  solid  or  liquid,  that  do  not  crystal- 
ize  regularly,  are  more  pervious  to  the  calorific  rays 
according  as  they  possess  a  greater  refractive  power. 
For  example,  the  chloride  of  sulphur,  which  has  a  high 
refractive  power,  transmits  more  of  the  calorific  rays  than 
the  oils,  which  have  a  less  refractive  power  :  oils  trans- 
mit more  radiant  heat  than  the  acids ;  the  acids  more 
than  aqueous  solutions ;  and  the  latter  more  than  pure 
water,  which  of  all  the  series  has  the  least  refractive 
power,  and  is  the  least  pervious  to  heat.  M.  Melloni 
observed  also,  that  each  ray  of  the  solar  spectrum  follows 
the  same  law  of  action  with  that  of  terrestrial  rays  hav- 


214  MAXIMUM  OF  HEAT  IN  SPECTRUM.     SECT.  XXV. 

ing  their  origin  in  sources  of  different  temperatures  ;  so 
that  the  very  refrangible  rays  may  be  compared  to  the 
heat  emanating  from  a  focus  of  high  temperature,  and 
the  least  refrangible  to  the  heat  which  comes  from  a 
source  of  low  temperature.  Thus  if  the  calorific  rays 
emerging  from  a  prism  be  made  to  pass  through  a  layer 
of  water  contained  between  two  plates  of  glass,  it  will 
be  found  that  these  rays  suffer  a  loss  in  passing  through 
the  liquid,  as  much  greater  as  their  refrangibility  is  less. 
The  rays  of  heat  that  are  mixed  with  the  blue  or  violet 
light  pass  in  great  abundance,  while  those  in  the  obscure 
part  which  follows  the  red  light  are  almost  totally  inter- 
cepted. The  first,  therefore,  act  like  the  heat  of  a 
lamp,  and  the  last  like  that  of  boiling  water. 

These  circumstances  explain  the  phenomena  observed 
by  several  philosophers  will  regard  to  the  point  of 
greatest  heat  in  the  solar  spectrum,  which  varies  with 
the  substance  of  the  prism.  Sir  William  Herschel, 
who  employed  a  prism  of  flint  glass,  found  that  point  to 
be  a  little  beyond  the  red  extremity  of  the  spectrum  : 
bat  according  to  M.  Seebeck,  it  is  found  to  be  upon  the 
yellow,  upon  the  orange,  on  the  red,  or  at  the  dark 
limit  of  the  red,  according  as  the  prism  consists  of 
water,  sulphuric  acid,  crown  or  flint  glass.  If  it  be 
recollected  that  in  the  spectrum  from  crown  glass,  the 
maximum  heat  is  in  the  red  part,  and  that  the  solar 
rays,  in  traversing  a  mass  of  water,  suffer  losses  inversely 
as  their  refrangibility,  it  will  be  easy  to  understand  the 
reason  of  the  phenomenon  in  question.  The  solar  heat 
which  comes  to  the  anterior  face  of  the  prism  of  water 
consists  of  rays  of  all  degrees  of  refrangibility.  Now, 
the  rays  possessing  the  same  index  of  refraction  with 
the  red  light  suffer  a  greater  loss  in  passing  through  the 
prism  than  the  rays  possessing  the  refrangibility  of  the 
orange  light,  and  the  latter  lose  less  in  their  passage  than 
the  heat  of  the  yellow.  Thus  the  losses,  being  inversely 
proportional  to  the  degree  of  refrangibility  of  each  ray, 
cause  the  point  of  maximum  heat  to  tend  from  the  red 
toward  the  violet,  and  therefore  it  rests  upon  the  yellow 
part.  The  prism  of  sulphuric  acid  acting  similarly,  but 
with  less  energy  than  that  of  water,  throws  the  point  of 
greatest  heat  on  the  orange  ;  for  the  same  reason,  tho 


SECT.  XXV  POLARIZATION  OF  CALORIC.  215 

crown  and  flint  glass  prisms  transfer  that  point  respec- 
tively to  the  red  and  to  its  limit.  M.  Melloni,  observing 
that  the  maximum  point  of  heat  is  transferred  farther 
and  farther  toward  the  red  end  of  the  spectrum,  ac- 
cording as  the  substance  of  the  prism  is  more  and  more 
permeable  to  heat,  inferred  that  a  prism  of  rock-salt, 
which  possesses  a  greater  power  of  transmitting  the 
calorific  rays  than  any  known  body,  ought  to  throw  the 
point  of  greatest  heat  to  a  considerable  distance  beyond 
the  visible  part  of  the  spectrum, — an  anticipation  which 
experiment  fully  confirmed,  by  placing  it  as  much  be- 
yond the  dark  limits  of  the  red  rays  as  the  red  part  is 
distant  from  the  bluish  green  band  of  the  spectrum. 

In  all  these  experiments,  M.  Melloni  employed  a 
thermo-multiplier, — an  instrument  that  measures  the 
intensity  of  the  transmitted  heat  with  an  accuracy  far 
beyond  what  any  thermometer  ever  attained.  It  is  a 
very  elegant  application  of  M.  Seebeck's  discovery  oi 
thermo-electricity;  but  the  description  of  this  instrument 
is  reserved  for  a  future  occasion,  because  the  principle 
on  which  it  is  constructed  has  not  yet  been  explained. 

In  the  beginning  of  the  present  century,  not  long  after 
M.  Malus  had  discovered  the  polarization  of  light,  he 
and  M.  Berard  proved  that  the  heat  which  accompanies 
the  sun's  light  is  capable  of  being  polarized  ;  but  their 
attempts  totally  failed  with  heat  derived  from  terrestrial, 
and  especially  from  non-luminous  sources.  M.  Berard, 
indeed,  imagined  that  he  had  succeeded ;  but  when  his 
experiments  were  repeated  by  Mr.  Lloyd  and  Professor 
Powell,  no  satisfactory  result  could  be  obtained.  M- 
Melloni  lately  resumed  the  subject,  and  endeavored  to 
effect  the  polarization  of  heat  by  tourmaline,  as  in  the 
case  of  light.  It  was  already  shown  that  two  slices  of 
tourmaline  cut  parallel  to  the  axis  of  the  crystal,  trans- 
mit a  great  portion  of  the  incident  light  when  looked 
through  with  their  axes  parallel,  and  almost  entirely  ex- 
clude it  when  they  are  perpendicular  to  one  another. 
Should  radiant  heat  be  capable  of  polarization,  the  quan- 
tity transmitted  by  the  slices  of  tourmaline  in  their  for- 
mer position  ought  greatly  to  exceed  that  which  passes 
through  them  in  the  latter,  yet  M.  Melloni  found  that 
the  quantity  of  heat  was  the  same  in  both  cases :  whence 


216  POLARIZATION  OF  CALORIC.  SECT.  XXV. 

he  inferred  that  heat  from  a  terrestrial  source  is  inca- 
pable of  being  polarized.  Professor  Forbes  of  Edin- 
burgh, who  has  recently  prosecuted  this  subject  with 
great  acuteness  and  success,  came  to  the  same  conclu- 
sion in  the  first  instance  ;  but  it  occurred  to  him,  that  as 
the  pieces  of  tourmaline  became  heated  by  being  very 
near  the  lamp,  the  secondary  radiation  from  them  ren- 
dered the  very  small  difference  in  the  heat  that  was 
transmitted  in  the  two  positions  of  the  tourmalines  im- 
perceptible. The  same  conclusion  had  been  come  at 
by  M.  Melloni ;  nevertheless  Mr.  Forbes  succeeded  in 
proving  by  numerous  observations,  that  heat  from  vari- 
ous sources  was  polarized  by  the  tourmaline  ;  but  that 
the  effect  with  non-luminous  heat  was  very  minute  and 
difficult  to  perceive,  on  account  of  the  secondary  radia- 
tion. Though  light  is  almost  entirely  excluded  in  one 
position  of  the  tourmalines,  and  transmitted  in  the  other, 
a  vast  quantity  of  radiant  heat  passes  through  them  in 
all  positions.  Eighty-four  per  cent,  of  the  heat  from  an 
argand  lamp  passed  through  the  tourmalines  in  the  case 
where  light  was  altogether  stopped.  It  is  only  the  dif- 
ference in  the  quantity  of  transmitted  heat  that  gives 
evidence  of  its  polarization.  The  second  slice  of  tour- 
maline, when  perpendicular  to  the  first,  stops  all  the 
light,  but  transmits  a  great  proportion  of  heat ;  alum,  on 
the  contrary,  stops  almost  all  the  heat  and  transmits  the 
light ;  whence  it  may  be  concluded  that  heat,  though 
intimately  partaking  the  nature  of  light,  and  accompany- 
ing it  under  certain  circumstances,  as  in  reflection  and 
refraction,  is  capable  of  almost  complete  separation  from 
it  under  others.  The  separation  has  since  been  per- 
fectly effected  by  M.  Melloni,  by  passing  a  beam  of  light 
through  a  combination  of  water  and  green  glass,  colored 
by  the  oxide  of  copper.  Even  when  the  transmitted 
light  was  concentrated  by  lenses,  so  as  to  render  it  almost 
as  brilliant  as  the  direct  light  of  the  sun,  it  showed  no 
sensible  heat. 

Professor  Forbes  next  employed  two  bundles  of  lam- 
inae of  mica,  placed  at  the  polarizing  angle,  and  so  cut 
that  the  plane  of  incidence  of  the  heat  corresponded 
with  one  of  the  optic  axes  of  this  mineral.  The  heat 
transmitted  through  this  apparatus  was  polarized  when, 


SECT.  XXV.          POLARIZATION  OF  CALORIC.  217 

from  a  source  whose  temperature  was  even  as  low  as 
200°,  heat  was  also  polarized  by  reflection ;  but  the  ex- 
periments, though  perfectly  successful,  are  more  diffi- 
cult to  conduct. 

It  appears  from  the  various  experiments  of  M.  Mel- 
loni  and  Professor  Forbes,  that  all  the  calorific  rays  ema- 
nating from  the  sun  and  terrestrial  sources  are  equally 
capable  of  being  polarized  by  reflection  and  by  refrac- 
tion, whether  double  or  simple,  and  that  they  are  also 
capable  of  circular  polarization  by  all  the  methods  em- 
ployed in  the  circular  polarization  of  light.  Plates  of 
quartz  cut  at  right  angles  to  the  axis  of  the  prism,  pos- 
sess the  property  of  turning  the  calorific  rays  in  any 
direction,  while  other  plates  of  the  same  substance  from 
a  differently  modified  prism  cause  the  rays  to  rotate  in 
the  contrary  direction ;  and  two  plates  combined,  when 
of  different  affection,  and  of  equal  thickness,  counteract 
each  other's  effects,  as  in  the  case  of  light.  Tourmaline 
separates  the  caloric  into  two  parts,  one  of  which  it  ab- 
sorbs, while  it  transmits  the  other ;  in  short,  the  trans- 
mission of  radiant  heat  is  precisely  similar  to  that  of  light. 

Since  heat  is  polarized  in  the  same  manner  as  light,  it 
may  be  expected  that  polarized  heat  transmitted  through 
doubly  refracting  substances  should  be  separated  into 
two  pencils,  polarized  in  planes  at  right  angles  to  each 
other ;  and  that  when  received  on  an  analyzing  plate 
they  should  interfere  and  produce  invisible  phenomena, 
perfectly  analogous  to  those  described  in  Section  XXII. 
with  regard  to  light  (N.  212). 

It  was  shown  in  the  same  section,  that  if  light  polar- 
ized by  reflection  from  a  pane  of  glass  be  viewed  through 
a  plate  of  tourmaline,  with  its  longitudinal  section  verti- 
cal, an  obscure  cloud,  with  its  center  wholly  dark,  is 
seen  on  the  glass.  When,  however,  a  plate  of  mica 
uniformly  about  the  thirteenth  of  an  Inch  in  thickness 
is  interposed  between  the  tourmaline  and  the  glass,  the 
dark  spot  vanishes,  and  a  succession  of  very  splendid 
colors  is  seen;  and  as  the  mica  is  turned  round  in  a 
plane  perpendicular  to  the  polarized  ray,  the  light  is 
stopped  when  the  plane  containing  the  optic  axis  of  the 
mica  is  parallel  or  perpendicular  to  the  plane  of  polar- 
ization. Now  instead  of  light,  if  heat  from  a  non-lumi~ 


218  POLARIZATION  OF  CALORIC.  SECT.  XXV. 

nous  source  be  polarized  in  the  manner  described,  it 
ought  td  be  transmitted  and  stopped  by  the  interposed 
mica  under  the  same  circumstances  under  which  polar- 
ized light  would  be  transmitted  or  stopped.  Prolessor 
Forbes  has  found  that  this  is  really  the  case,  whether  he 
employed  heat  from  luminous  or  non-luminous  sources : 
and  he  had  evidence  also  of  circular  and  elliptical  polar- 
ization of  heat.  It  therefore  follows  that  if  heat  were 
visible,  under  similar  circumstances  we  should  see  fig- 
ures perfectly  similar  to  those  given  in  Note  207,  and 
those  following;  and  as  these  figures  are  formed  by  the 
interference  of  undulations  of  light,  it  may  be  inferred 
that  heat,  like  light,  is  propagated  by  undulations  of  the 
ethereal  medium,  which  interfere  under  certain  condi- 
tions, and  produce  figures  analogous  to  those  of  light. 
It  appears  also  from  Mr.  Forbes's  experiments,  that  the 
undulations  of  heat  are  probably  longer  than  the  undu- 
lations of  light. 

Since  the  power  of  penetrating  glass  increases  in  pro- 
portion as  the  radiating  caloric  approaches  the  slate  of 
light,  it  seemed  to  indicate  that  the  same  principle  takes 
the  form  of  light  or  heat  according  to  the  modification 
it  receives,  and  that  the  hot  rays  are  only  invisible  light; 
and  light,  luminous  caloric.  It  was  natural  to  infer,  that 
in  the  gradual  approach  of  invisible  caloric  to  the  condi- 
tion and  properties  of  luminous  caloric,  the  invisible 
rays  must  at  first  be  analogous  to  the  least  calorific  part 
of  the  spectrum,  which  is  at  the  violet  extremity — an 
analogy  which  appeared  to  be  greater,  by  all  flame 
being  at  first  violet  or  blue,  and  only  becoming  white 
when  it  has  attained  its  greatest  intensity.  Thus,  as 
diaphanous  bodies  transmit  light  with  the  same  facility 
whether  proceeding  from  the  sun  or  from  a  glowworm, 
and  as  no  substance  had  hitherto  been  found  which  in- 
stantaneously transmits  radiant  caloric  coming  from  a 
source  of  low  temperature,  it  was  concluded  that  no 
such  substance  exists,  and  the  great  difference  between 
the  transmission  of  light  and  radiant  heat  was  thus  re- 
ferred to  the  nature  of  the  agent  of  heat,  and  not  to  the 
action  of  matter  upon  the  calorific  rays.  M.  Melloni, 
however,  has  discovered  in  rock-salt  a  substance  which 
transmits  radiant  heat  with  the  same  facility  whether  it 


SBCT.  XXV.  NATURE  OF  CALORIC.  219 

originates  in  the  brightest  flame  or  lukewarm  water, 
and  which  consequently  possesses  the  same  permeability 
with  regard  to  heat  that  all  diaphanous  bodies  have  for 
light.  It  follows,  therefore,  that  the  impermeability  of 
glass  and  other  substances  for  radiant  heat  arises  from 
their  action  upon  the  calorific  rays,  and  not  from  the 
principle  of  caloric.  But  although  this  discovery  changes 
the  received  ideas  drawn  from  M.  de  Laroche's  experi- 
ments, it  establishes  a  new  and  unlooked-for  analogy 
between  these  two  great  agents  of  nature.  True  it  is 
that  the  separation  of  the  luminous  and  calorific  rays 
shows  that  they  must  owe  their  immediate  origin  to  two 
different  causes,  at  the  same  time  it  is  quite  possible 
that  these  two  causes  themselves  may  be  only  different 
effects  of  one  single  cause.  The  probability  of  light  and 
heat  being  modifications  of  the  same  principle  is  not 
diminished  by  the  calorific  rays  being  unseen,  for  the 
condition  of  visibility  or  invisibility  may  only  depend 
upon  the  construction  of  our  eyes,  and  not  upon  the 
nature  of  the  agent  which  produces  these  sensations  in 
us.  The  sense  of  seeing  may  be  confined  within  certain 
limits.  The  chemical  rays  beyond  the  violet  end  of  the 
spectrum  may  be  too  rapid,  or  not  sufficiently  excursive 
in  their  vibrations  to  be  visible  to  the  human  eye  ;  and 
the  calorific  rays  beyond  the  other  end  of  the  spectrum 
may  not  be  sufficiently  rapid,  or  too  extensive,  in  their 
undulations,  to  affect  our  optic  nerves,  though  both  may 
be  visible  to  certain  animals  or  insects.  We  are  alto- 
gether ignorant  of  the  perceptions  which  direct  the  car- 
rier-pigeon to  his  home,  or  of  those  in  the  antennae  of 
insects  which  warn  them  of  the  approach  of  danger; 
nor  can  we  understand  the  telescopic  vision  which  di- 
rects the  vulture  to  his  prey  before  he  himself  is  visible 
even  as  a  speck  in  the  heavens  (N.  213).  So  likewise 
beings  may  exist  on  earth,  in  the  air,  or  in  the  waters, 
which  hear  sounds  our  ears  are  incapable  of  hearing, 
and  which  see  rays  of  light  and  heat  of  which  we  are 
unconscious.  Our  perceptions  and  faculties  are  limited 
to  a  very  small  portion  of  that  immense  chain  of  exist- 
ence which  extends  from  the  Creator  to  evanescence. 

The  identity  of  action  under  similar  circumstances  is 
one  of  the  strongest  arguments  in  favor  of  the  common 


220  ABSORPTION  OF  CALORIC.  SECT.  XXV. 

nature  of  the  chemical,  visible,  and  calorific  rays.  They 
are  all  capable  of  reflection  from  polished  surfaces,  of 
refraction  through  diaphanous  substances,  of  polarization 
by  reflection  and  by  doubly  refracting  crystals  :  none  of 
these  rays  add  sensibly  to  the  weight  of  matter;  their 
velocity  is  prodigious ;  they  may  be  concentrated  and 
dispersed  by  convex  and  concave  mirrors ;  they  pass 
with  equal  facility  through  rock-salt,  and  are  capable  of 
radiation ;  the  chemical  rays  are  subject  to  the  same 
law  of  interference  with  those  of  light ;  and  although 
the  interference  of  the  calorific  rays  has  not  yet  been 
proved  directly,  the  indirect  evidence  places  it  beyond  a 
doubt.  As  the  action  of  matter  in  so  many  cases  is  the 
same  on  the  whole  assemblage  of  rays,  visible  and 
invisible,  which  constitute  a  solar  beam,  it  is  more  than 
probable  that  the  obscure  as  well  as  the  luminous  part  is 
propagated  by  the  undulations  of  an  imponderable  ether, 
and  consequently  comes  under  the  same  laws  of  analysis. 
When  radiant  heat  falls  upon  a  surface,  part  of  it  is 
reflected  and  part  of  it  is  absorbed ;  consequently  the 
best  reflectors  possess  the  least  absorbing  powers.  The 
temperature  of  very  transparent  fluids  is  not  raised  by 
the  passage  of  the  sun's  rays,  because  they  do  not 
absorb  any  of  them  :  and  as  his  heat  is  very  intense, 
transparent  solids  arrest  a  very  small  portion  of  it. 
The  absorption  of  the  sun's  rays  is  the  cause  both  of 
the  color  and  temperature  of  solid  bodies.  A  black 
substance  absorbs  all  the  rays  of  light  and  reflects  none; 
and  since  it  absorbs  at  the  same  time  all  the  calorific 
rays,  it  becomes  sooner  warm,  and  rises  to  a  higher 
temperature  than  bodies  of  any  other  color.  Blue 
bodies  come  next  to  black  in  their  power  of  absorption. 
Of  all  the  colors  of  the  solar  spectrum,  the  blue  pos- 
sesses least  of  the  heating  power ;  and  since  substances 
of  a  blue  tint  absorb  all  the  other  colors  of  the  spectrum, 
they  absorb  by  far  the  greatest  part  of  the  calorific  rays, 
and  reflect  the  blue  where  they  are  least  abundant. 
Next  in  order  come  the  green,  yellow,  red,  and  last  of 
all,  white  bodies,  which  reflect  nearly  all  the  rays  both 
of  light  and  heat.  However,  there  are  certain  limpid 
and  colorless  media,  which  in  some  cases  intercept 
calorific  radiations  and  become  heated,  while  in  other 


SECT.  XXV.      ABSORPTION  OF  CALORIC— DEW.  221 

cases  they  transmit  them  and  undergo  no  change  of 
temperature. 

All  substances  may  be  considered  to  radiate  caloric, 
whatever  their  temperature  may  be,  though  with  dif- 
ferent intensities,  according  to  their  nature,  the  state  of 
their  surfaces,  and  the  temperature  of  the  medium  into 
which  they  are  brought.  But  eveiy  surface  absorbs  as 
well  as  radiates  caloric  ;  and  the  power  of  absorption 
is  always  equal  to  that  of  radiation ;  for  under  the  same 
circumstances,  matter  which  becomes  soon  warm  also 
cools  rapidly.  There  is  a  constant  tendency  to  an 
equal  diffusion  of  caloric,  since  every  body  in  nature  is 
giving  and  receiving  it  at  the  same  instant :  each  will  be 
of  uniform  temperature  when  the  quantities  of  caloric 
given  and  received  during  the  same  time  are  equal, — 
that  is,  when  a  perfect  compensation  takes  place  be- 
tween each  and  all  the  rest.  Our  sensations  only 
measure  comparative  degrees  of  heat:  when  a  body, 
such  as  ice,  appears  to  be  cold,  it  imparts  fewer  calorific 
rays  than  it  receives  ^  and  when  a  substance  seems  to 
be  warm, — for  example,  a  fire, — it  gives  more  caloric 
than  it  takes.  The  phenomena  of  dew  and  hoar-frost 
are  owing  to  this  inequality  of  exchange ;  the  caloric 
radiated  during  the  night  by  substances  on  the  surface 
of  the  earth  into  a  clear  expanse  of  sky  is  lost,  and  no 
return  is  made  from  the  blue  vault,  so  that  their  tem- 
perature sinks  below  that  of  the  air,  whence  they 
abstract  a  part  of  that  caloric  which  holds  the  atmos- 
pheric humidity  in  solution,  and  a  deposition  of  dew 
takes  place.  If  the  radiation  be  great,  the  dew  is 
frozen  and  becomes  hoar-frost,  which  is  the  ice  of  dew. 
Cloudy  weather  is  unfavorable  to  the  formation  of  dew, 
by  preventing  the  free  radiation  of  caloric ;  and  actual 
contact  is  requisite  for  its  deposition,  since  it  .is  never 
suspended  in  the  air  like  fog.  Plants  derive  a  great 
part  of  their  nourishment  from  this  source  ;  and  as  each 
possesses  a  power  of  radiation  peculiar  to  itself,  they 
are  capable  of  procuring  a  sufficient  supply  for  their 
wants.  The  action  of  the  chemical  rays  imparts  to  all 
substances  more  or  less  the  power  of  condensing  vapor 
on  tlwse  parts  on  which  they  fall,  and  must  therefore 
have  a  considerable  influence  on  the  deposition  of  dew. 

T2 


222  RAIN— COMBUSTION.  SECT.  XXV. 

Ram  is  formed  by  the  mixing  of  two  masses  of  air  of 
different  temperatures;  the  colder  part,  by  abstracting 
from  the  other  the  heat  which  holds  it  in  solution,  occa- 
sions the  particles  to  approach  each  other  and  form 
drops  of  water,  vwhich,  becoming  too  heavy  to  be  sus- 
tained by  the  atmosphere,  sink  to_  the  earth  by  gravita- 
tion in,  the  form  of  rain.  The  contact  of  two  strata  of 
air  of  different  temperatures,  moving  rapidly  in  opposite 
directions,  occasions  an  abundant  precipitation  of  rain. 
When  the  masses  of  air  differ  very  much  in  tempera- 
ture, and  meet  suddenly,  hail  is  formed.  This  happens 
frequently  in  hot  plains  near  a  ridge  of  mountains,  as  in 
the  south  of  France ;  but  no  explanation  has  hitherto 
been  given  of  the  cause  of  the  severe  hail-storms  which 
occasionally  take  place  on  extensive  plains  within  the 
tropics. 

An  accumulation  of  caloric  invariably  produces  light : 
with  the  ^exception  of  the  gases,  all  bodies  which  can 
endure  the  requisite  degree  of  heat  without  decompo- 
sition begin  to  emit  light  at  the  same  temperature ;  but 
when  the  quantity  of  caloric  is  so  great  as  to  render  the 
affinity  of  their  component  particles  less  than  their 
affinity  for  the  oxygen  of  the  atmosphere,  a  chemical 
combination  takes  place  with  the  oxygen,  light  and  heat 
are  evolved,  and  fire  is  produced.  Combustion — so 
essential  for  our  comfort,  and  even  existence — takes 
place  very  easily  from  the  small  affinity  between  the 
component  parts  of  atmospheric  air,  the  oxygen  being 
nearly  in  a  free  state ;  but  as  the  cohesive  force  of  the 
particles  of  different  substances  is  very  variable,  differ- 
ent degrees  of  heat  are  requisite  to  produce  their  com- 
bustion. The  tendency  of  heat  to  a  state  of  equal 
diffusion  or  equilibrium,  either  by  radiation  or  contact, 
makes  it  necessary  that  the  chemical  combination  which 
occasions  combustion  should  take  place  instantaneously ; 
for  if  the  heat  were  developed  progressively,  it  would 
be  dissipated  by  degrees,  and  would  never  accumulate 
sufficiently  to  produce  a  temperature  high  enough  for 
the  evolution  of  flame. 

It  is  a  general  law  that  all  bodies  expand  by  heat  and 
contract  by  cold.  The  expansive  force  of  tfaloric  has  a 
constant  tendency  to  overcome  the  attraction  of  cohesion, 


SICT.  XXV.  EXPANSION.  223 

and  to  separate  the  constituent  particles  of  solids  and 
fluids ;  by  this  separation  the  attraction  of  aggregation  is 
more  and  more  weakened,  till  at  last  it  is  entirely  over- 
come, or  even  changed  into  repulsion.  By  the  continual 
addition  of  caloric,  solids  may  be  made  to  pass  into  liquids, 
and  from  liquids  to  the  aeriform  state,  the  dilatation  in- 
creasing with  the  temperature  ;  and  every  substance  ex- 
pands according  to  a  law  of  its  own.  Gases  expand  more 
than  liquids,  and  liquids  more  than  solids.  The  expan- 
sion of  air  is  more  than  eight  times  that  of  water,  and  the 
increase  in  the  bulk  of  water  is  at  least  forty-five  times 
greater  than  that  of  iron.  Metals  dilate  uniformly  from 
the  freezing  to  the  boiling  points  of  the  thermometer ; 
the  uniform  expansion  of  the  gases  extends  between  still 
wider  limits ;  but  as  liquidity  is  a  state  of  transition  from 
the  solid  to  the  ae'riform  condition,  the  equable  dilatation 
of  liquids  has  not  so  extensive  a  range.  This  change  of 
bulk,  corresponding  to  the  variation  of  heat,  is  one  of  the 
most  important  of  its  effects,  since  it  furnishes  the  means 
of  mejisuring  relative  temperature  by  the  thermometer 
and  pyrometer.  The  rate  of  expansion  of  solids  varies 
at  their  transition  to  liquidity,  and  that  of  liquidity  is  no 
longer  equable  near  their  change  to  an  aeriform  state. 
There  are  exceptions  however  to  the  general  laws  of 
expansion ;  some  liquids  have  a  maximum  density  corres- 
ponding to  a  certain  temperature,  and  dilate  whether  that 
temperature  be  increased  or  diminished.  For  example 
— water  expands  whether  it  be  heated  above  or  cooled 
below  40°.  Tha  solidification  of  some  liquids,  and  es- 
pecially their  crystalization,  is  always  accompanied  by  an 
increase  of  bulk.  Water  dilates  rapidly  when  converted 
into  ice,  and  with  a  force  sufficient  to  split  the  hardest 
substances.  The  formation  of  ice  is  therefore  a  pow- 
erful agent  in  the  disintegration  and  decomposition  of 
rocks,  operating  as  one  of  the  most  efficient  causes  of 
local  changes  in  the  structure  of  the  crust  of  the  earth  ; 
of  which  we  have  experience  in  the  tremendous  eboule- 
tnents  of  mountains  in  Switzerland. 

The  dilatation  of  substances  by  heat,  and  their  con- 
traction by  cold,  occasion  such  irregularities  in  the  rate 
of  clocks  and  watches  as  would  render  them  unfit  for 
astronomical  or  nautical  purposes,  were  it  not  for  a  very 


224  COMPENSATION  PENDULUM.  SECT.  XXV. 

beautiful  application  of  the  laws  of  unequal  expansion. 
The  oscillations  of  a  pendulum  are  the  same  as  if  its 
whole  mass  were  united  in  one  dense  particle,  in  a  cer- 
tain point  of  its  length,  called  the  center  of  oscillation. 
If  the  distance  of  this  point  from  the  point  by  which  the 
pendulum  is  suspended  were  invariable,  the  rate  of  the 
clock  would  be  invariable  also.  The  difficulty  is  to  neu- 
tralize the  effects  of  temperature,  which  is  perpetually 
increasing  or  diminishing  its  length.  Among  many  con- 
trivances, Graham's  compensation  pendulum  is  the  most 
simple.  He  employed  a  glass  tube  containing  mercury. 
When  the  tube  expands  from  the  effects  of  heat,  the 
mercury  expands  much  more ;  so  that  its  surface  rises 
a  little  more  than  the  end  of  the  pendulum  is  depressed, 
and  the  center  of  oscillation  remains  stationary.  Har- 
rison invented  a  pendulum  which  consists  of  seven  bars 
of  steel  and  of  brass,  joined  in  the  shape  of  a  gridiron, 
in  such  a  manner  that  if  by  change  of  temperature  the 
bars  of  brass  raise  the  weight  at  the  end  of  the  pendu- 
lum, the  bars  of  steel  depress  it  as  much.  In  general, 
only  five  bars  are  used  ;  three  being  of  steel  and  two  a 
mixture  of  silver  and  zinc.  The  effects  of  temperature 
are  neutralized  in  chronometers  upon  the  same  princi- 
ple ;  and  to  such  perfection  are  they  brought,  that  the 
loss  or  gain  of  one  second  in  twenty-four  hours  for  two 
days  running  would  render  one  unfit  for  use.  Accuracy 
in  surveying  depends  upon  the  compensation  rods  em- 
ployed in  measuring  bases.  Thus,  the  laws  of  the  une- 
qual expansion  of  matter  judiciously  applied  have  an 
immediate  influence  upon  our  estimation  of  time :  of 
the  motions  of  bodies  in  the  heavens,  and  of  their  fall 
upon  the  earth ;  on  our  determination  of  the  figure  of 
the  globe,  and  on  our  system  of  weights  and  measures  ; 
on  our  commerce  abroad,  and  the  mensuration  of  our 
lands  at  home. 

The  expansion  of  the  crystaline  substances  takes  place 
under  very  different  circumstances  from  the  dilatation 
of  such  as  are  not  crystalized.  The  latter  become  both 
longer  and  thicker  by  an  acession  of  heat,  whereas  M. 
Mitscherlich  has  found  that  the  former  expand  differ- 
ently in  different  directions  ;  and  in  a  particular  instance, 
extension  in  one  direction  is  accompanied  by  contraction 


SECT.  XXV.  PROPAGATION  OF  HEAT.  225 

in  another.  The  internal  structure  of  crystalized  mat- 
ter must  be  very  peculiar,  thus  to  modify  the  expansive 
power  of  heat,  and  so  materially  to  influence  the  trans- 
mission of  caloric  and  the  visible  rays  of  the  spectrum. 

Heat  is  propagated  with  more  or  less  rapidity  through 
all  bodies ;  air  is  the  worst  conductor,  and  consequently 
mitigates  the  severity  of  cold  climates  by  preserving  the 
heat  imparted  to  the  earth  by  the  sun.  On  the  con- 
trary, dense  bodies,  especially  metals,  possess  the  power 
of  conduction  in  the  greatest  degree,  but  the  transmis- 
sion requires  time.  If  a  bar  of  iron  twenty  inches  long 
be  heated  at  one  extremity,  the  caloric  takes  four  min- 
utes in  passing  to  the  other.  The  particle  of  the  metal 
that  is  first  heated  communicates  its  caloric  to  the  sec- 
ond, and  the  second  to  the  third ;  so  that  the  temperature 
of  the  intermediate  molecule  at  any  instant  is  increased 
by  the  excess  of  the  temperature  of  the  first  above  its 
own,  and  diminished  by  the  excess  of  its  own  tempera- 
ture above  that  of  the  third.  That  however  will  not 
be  the  temperature  indicated  by  the  thermometer,  be- 
cause as  soon  as  the  particle  is  more  heated  than  the 
surrounding  atmosphere,  it  loses  its  caloric  by  radiation, 
in  proportion  to  the  excess  of  its  actual  temperature 
above  that  of  the  air.  The  velocity  of  the  discharge  is 
directly  proportional  to  the  temperature,  and  inversely 
as  the  length  of  the  bar.  As  there  are  perpetual  varia- 
tions in  the  temperature  of  all  terrestrial  substances  and 
of  the  atmosphere,  from  the  rotation  of  the  earth,  and 
its  revolution  round  the  sun,  from  combustion,  friction, 
fermentation,  electricity,  and  an  infinity  of  other  causes, 
the  tendency  to  restore  the  equability  of  temperature 
by  the  transmission  of  caloric  must  maintain  all  the 
particles  of  matter  in  a  state  of  perpetual  oscillation, 
which  will  be  more  or  less  rapid  according  to  the  con- 
ducting powers  of  the  substances.  From  the  motion  of 
the  heavenly  bodies  about  then*  axes,  and  also  round  the 
sun,  exposing  them  to  perpetual  changes  of  temperature, 
it  may  be  inferred  that  similar  causes  will  produce  like 
effects  in  them  too.  The  revolutions  of  the  double  stars 
show  that  they  are  not  at  rest ;  and  though  we  are  to- 
tally ignorant  of  the  changes  that  may  be  going  on  in  the 
nebulae  and  millions  of  other  remote  bodies,  it  is  hardly 
15 


226  PROPAGATION  OF  HEAT.  SECT.  XXV. 

possible  that  they  should  be  in  absolute  repose ;  so  that, 
as  far  as  our  knowledge  extends,  motion  seems  to  be  a 
law  of  matter. 

Heat  applied  to  the  surface  of  a  fluid  is  propagated 
downward  very  slowly,  the  warmer  and  consequently 
lighter  strata  always  remaining  at  the  top.  This  is  the 
reason  why  the  water  at  the  bottom  of  lakes  fed  from 
alpine  chains  is  so  cold  ;  for  the  heat  of  the  sun  is  trans- 
fused but  a  little  way  below  the  surface.  "When  heat 
is  applied  below  a  liquid,  the  particles  continually  rise 
as  they  become  specifically  lighteir  in  consequence  of 
the  caloric,  and  diffuse  it  through  the  mass,  their  place 
being  perpetually  supplied  by  those  that  are  more  dense. 
The  power  of  conducting  heat  varies  materially  in  dif- 
ferent liquids.  Mercury  conducts  twice  as  fast  as  an 
equal  bulk  of  water,  which  is  the  reason  why  it  appears 
to  be  so  cold.  A  hot  body  diffuses  its  caloric  in  the  ah* 
by  a  double  process.  The  air  in  contact  with  it  being 
heated  and  becoming  lighter,  ascends  and  scatters  its 
caloric,  while  at  the  same  time  another  portion  is  dis- 
charged in  straight  lines  by  the  radiating  powers  of  the 
surface.  Hence  a  substance  cools  more  rapidly  in  air 
than  in  vacuo,  because  in  the  latter  case  the  process  is 
carried  on  by  radiation  alone.  It  is  probable  that  the 
earth,  having  originally  been  of  very  high  temperature, 
has  become  cooler  by  radiation  only.  The  ethereal 
medium  must  be  too  rare  to  carry  off  much  caloric. 

Besides  the  degree  of  heat  indicated  by  the  thermom- 
eter, caloric  pervades  bodies  in  an  imperceptible  or  latent 
state  ;  and  their  capacity  for  heat  is  so  various,  that  veiy 
different  quantities  of  caloric  are  required  to  raise  differ- 
ent substances  to  the  same  sensible  temperature ;  it  is 
therefore  evident  that  much  of  the  caloric  is  absorbed, 
or  becomes  latent  and  insensible  to  the  thermometer. 
The  portion  of  caloric  requisite  to  raise  a  body  to  a  given 
temperature  is  its  specific  heat ;  but  latent  heat  is  that 
portion  of  caloric  which  is  employed  in  changing  the  state 
of  bodies  from  solid  to  liquid,  and  from  liquid  to  vapor. 
When  a  solid  is  converted  into  a  liquid,  a  greater  quan- 
tity of  caloric  enters  into  it  than  can  be  detected  by  the 
thermometer ;  this  accession  of  caloric  does  not  make 
the  body  warmer,  though  it  converts  it  into  a  liquid,  and 


SKCT.  XXV.  LATENT  HEAT.  227 

is  the  principal  cause  of  its  fluidity.  Ice  remains  at  the 
temperature  of  32°  of  Fahrenheit  till  it  has  combined 
with  or  absorbed  140°  of  caloric,  and  then  it_melts,  but 
without  raising  the  temperature  of  the  water  above  32°  ; 
so  that  water  is  a  compound  of  ice  and  caloric.  On 
the  contrary,  when  a  liquid  is  converted  into  a  solid,  a 
quantity  of  caloric  leaves  it  without  any  diminution  of 
temperature.  Water  at  the  temperature  of  32°  must 
part  with  140°  of  caloric  before  it  freezes.  The  slow- 
ness with  which  water  freezes,  or  ice  thaws,  is  a  con- 
sequence of  the  time  required  to  give  out  or  absorb  140° 
of  latent  heat.  A  considerable  degree  of  cold  is  often  felt 
during  a  thaw,  because  the  ice,  in  its  transition  from  a 
solid  to  a  liquid  state,  absorbs  sensible  heat  from  the  atmos- 
phere and  other  bodies,  and  by  rendering  it  latent  main- 
tains them  at  the  temperature  of  32°  while  melting.  Ac- 
cording to  the  same  principle,  vapor  is  a  combination  of 
caloric  with  a  liquid.  By  the  continued  application  of 
heat,  liquids  are  converted  into  vapor  or  steam,  which 
is  invisible  and  elastic  like  common  air.  Under  the 
ordinary  pressure  of  the  atmosphere,  that  is,  when  the 
barometer  stands  at  30  inches,  water  acquires  a  constant 
accession  of  heat  till  its  temperature  rises  to  212°  of 
Fahrenheit ;  after  that  it  ceases  to  show  any  increase 
in  heat,  but  when  it  has  absorbed  an  additional  1000°  of 
caloric  it  is  converted  into  steam.  Consequently,  about 
1000°  of  latent  heat  exists  in  steam  without  raising  its 
temperature,  and  steam  at  212°  must  part  with  the  same 
quantity  of  latent  caloric  when  condensed  into  water. 
Water  boils  at  different  temperatures  under  different 
degrees  of  pressure.  It  boils  at  a  lower  temperature 
on  the  top  of  a  mountain  than  in  the  plain  below, 
because  the  weight  of  the  atmosphere  is  less  at  the 
higher  station.  There  is  no  limit  to  the  temperature 
to  which  water  might  be  raised ;  it  might  even  be  made 
red-hot,  could  a  vessel  be  found  strong  enough  to  resist 
the  pressure.  The  expansive  force  of  steam  is  in  pro- 
portion to  the  temperature  at  which  the  water  boils  ;  it 
may  therefore  be  increased  to  a  degree  that  is  only  lim- 
ited by  our  inability  to  restrain  it,  and  is  the  greatest 
power  that  has  been  made  subservient  to  the  wants  of 
man. 


228  STEAM.  SECT.  XXV. 

It  is  found  that  the  absolute  quantity  of  heat  consumed 
in  the  process  of  converting  water  into  steam  is  the  same 
at  whatever  temperature  water  may  boil,  but  that  the 
latent  heat  of  steam  is  always  greater  exactly  in  the  same 
proportion  as  its  sensible  heat  is  less.  Steam  raised  at 
212°  under  the  ordinary  pressure  of  the  atmosphere, 
and  steam  raised  at  180°  under  half  that  pressure,  con- 
tain the  same  quantity  of  heat,  with  this  difference,  that 
the  one  has  more  latent  heat  and  less  sensible  heat  than 
the  other.  It  is  evident  that  the  same  quantity  of  heat 
is  requisite  for  converting  a  given  weight  of  water  into 
steam,  at  whatever  temperature  or  under  whatever 
pressure  the  water  may  be  boiled ;  and  therefore  in  the 
steam  engine,  equal  weights  of  steam  at  a  high  pressure 
and  a  low  pressure  are  produced  by  the  same  quantity 
of  fuel ;  and  whatever  the  pressure  of  the  steam  may 
be,  the  consumption  of  fuel  is  proportional  to  the  quan- 
tity of  water  converted  into  vapor.  Steam  at  a  high 
pressure  expands  as  soon  as  it  comes  into  the  air,  by 
which  some  of  its  sensible  heat  becomes  latent ;  and  as 
it  naturally  has  less  sensible  heat  than  steam  raised  under 
low  pressure,  its  actual  temperature  is  reduced  so  much 
that  the  hand  may  be  plunged  into  it  without  injury  the 
instant  it  issues  from  the  orifice  of  a  boiler. 

The  elasticity  or  tension  of  steam,  like  that  of  common 
air,  varies  inversely  as  its  volume  ;  that  is,  when  the 
space  it  occupies  is  doubled,  its  elastic  force  is  reduced 
one-half.  The  expansion  of  steam  is  indefinite  ;  the 
smallest  quantity  of  water  when  reduced  to  the  form  of 
vapor,  will  occupy  many  millions  of  cubic  feet ;  a  wonder- 
ful illustration  of  the  minuteness  of  the  ultimate  parti- 
cles of  matter !  The  latent  heat  absorbed  in  the  forma- 
tion of  steam  is  given  out  again  by  its  condensation. 

Steam  is  formed  throughout  the  whole  mass  of  a 
boiling  liquid,  whereas  evaporation  takes  place  only  at 
the  free  surfaces  of  liquids,  and  that  under  the  ordinary 
temperature  and  pressure  of  the  atmosphere.  There 
is  a  constant  evaporation  from  the  land  and  water  all 
over  the  earth.  The  rapidity  of  its  formation  does  not 
altogether  depend  upon  the  dryness  of  the  air ;  according 
to  Dr.  Dalton's  experiments,  it  depends  also  on  the  dif- 
ference between  the  tension  of  the  vapor  which  is  form- 


S*CT.  XXV.  APPLICATION  OF  HEAT.  229 

ing  and  that  which  is  already  in  the  atmosphere.  In 
calm  weather,  vapor  accumulates  in  the  stratum  of  air 
immediately  above  the  evaporating  surface,  and  retards 
the  formation  of  more  ;  whereas  a  strong  wind  accele- 
rates the  process,  by  carrying  off  the  vapor  as  soon  as 
it  rises,  and  making  way  for  a  succeeding  portion  of 
dry  air. 

The  latent  heat  of  ah*  and  all  elastic  fluids  may  be 
forced  out  by  sudden  compression,  like  squeezing  water 
out  of  sponge.  The  quantity  of  heat  brought  into  action 
in  this  way  is  very  well  illustrated  hi  the  experiment  of 
igniting  a  piece  of  timber  by  the  sudden  compression  of 
air  by  a  piston  thrust  into  a  cylinder  closed  at  one  end  : 
the  development  of  heat  on  a  stupendous  scale  is  exhib- 
ited in  lightning,  probably  produced  in  part  by  the  violent 
compression  of  the  atmosphere  during  the  passage  of 
the  electric  fluid.  Prodigious  quantities  of  heat  are 
constantly  becoming  latent,  or  are  disengaged  by  the 
changes  of  condition  to  which  substances  are  liable  in 
passing  from  the  solid  to  the  liquid,  and  from  the  liquid 
to  the  gaseous  form,  or  the  contrary,  occasioning  endless 
vicissitudes  of  temperature  over  the  globe. 

There  are  many  other  sources  of  heat,  such  as  com- 
bustion, friction,  and  percussion,  all  of  which  are  only 
means  of  calling  a  power  into  evidence  which  already 
exists. 

The  application  of  heat  to  the  various  branches  of  the 
mechanical  and  chemical  arts  has,  within  a  few  years, 
effected  a  greater  change  in  the  condition  of  man  than 
had  been  accomplished  in  any  equal  period  of  his  exist- 
ence. Armed  by  the  expansion  and  condensation  of 
fluids  with  a  power  equal  to  that  of  the  lightning  itself, 
conquering  time  and  space,  he  flies  over  plains,  and  trav- 
els on  paths  cut  by  human  industry  even  through  moun- 
tains, with  a  velocity  and  smoothness  more  like  planetary 
than  terrestrial  motion  ;  he  crosses  the  deep  hi  opposi- 
tion to  wind  and  tide  ;  by  releasing  the  strain  on  the 
cable,  he  rides  at  anchor  fearless  of  the  storm  ;  he  makes 
the  elements  of  air  and  water  the  carriers  of  warmth, 
not  only  to  banish  winter  from  his  home,  but  to  adorn  it 
even  during  the  snow-storm  with  the  blossoms  of  spring; 
and,  like  a  magician,  he  raises,  from  the  gloomy  and 
U 


230  SIMILARITY  OF  LIGHT,  HEAT,  ETC.    SECT.  XXV. 

deep  abyss  of  the  mine,  the  spirit  of  light  to  dispel  the 
midnight  darkness. 

It  has  been  observed  that  heat,  like  light  and  sound, 
probably  consists  in  the  undulations  of  an  elastic  medium. 
All  the  principal  phenomena  of  heat  may  actually  be 
illustrated  by  a  comparison  with  those  of  sound.  The 
excitation  of  heat  and  sound  are  not  only  similar  but 
often  identical,  as  in  friction  and  percussion ;  they  are 
both  communicated  by  contact  and  radiation ;  and  Dr. 
Young  observes,  that  the  effect  of  radiant  heat  in  raising 
the  temperature  of  a  body  upon  which  it  falls,  resembles 
the  sympathetic  agitation  of  a  string  when  the  sound  of 
another  string  which  is  in  unison  with  it  is  transmitted 
through  the  air.  Light,  heat,  sound,  and  the  waves  of 
fluids,  are  all  subject  to  the  same  laws  of  reflection,  and 
indeed  their  undulatory  theories  are  perfectly  similar. 
If,  therefore,  we  may  judge  from  analogy,  the  undula- 
tions of  some  of  the  heat-producing  rays  must  be  less 
frequent  than  those  of  the  extreme  red  of  the  solar  spec- 
trum ;  but  the  analogy  is  now  perfect,  since  the  inter- 
ference of  heat  is  no  longer  a  matter  of  doubt :  hence 
the  interference  of  two  hot  rays  must  produce  cold  ; 
darkness  results  from  the  interference  of  two  undula- 
tions of  light ;  silence  ensues  from  the  interference  of 
two  undulations  of  sound ;  and  still  water,  or  no  tide,  is 
the  consequence  of  the  interference  of  two  tides.  The 
propagation  of  sound,  however,  requires  a  much  denser 
medium  than  that  either  of  light  or  heat ;  its  intensity 
diminishes  as  the  rarity  of  the  air  increases  ;  so  that,  at 
a  very  small  height  above  the  surface  of  the  earth,  the 
noise  of  the  tempest  ceases,  and  the  thunder  is  heard 
no  more  in  those  boundless  regions  where  the  heavenly 
bodies  accomplish  their  periods  in  eternal  and  sublime 
silence. 

A  consciousness  of  the  fallacy  of  our  senses  is  one  of 
the  most  important  consequences  of  the  study  of  nature. 
This  study  teaches  us  that  no  object  is  seen  by  us  in  its 
true  place,  owing  to  aberration ;  that  the  colors  of  sub- 
stances are  solely  the  effects  of  the  action  of  matter  upon 
light ;  and  that  light  itself,  as  well  as  heat  and  sound,  are 
not  real  beings,  but  mere  modes  of  action  communicated 
to  our  perceptions  by  the  nerves.  The  human  frame 


Sccr.  XXV.  HERSCHEI/S  EXPERIMENTS.  231 

may  therefore  be  regarded  as  an  elastic  system,  the  dif- 
ferent parts  of  which  are  capable  of  receiving  the  tremors 
of  elastic  media,  and  of  vibrating  in  unison  with  any  num- 
ber of  superposed  undulations,  all  of  which  have  their 
perfect  and  independent  effect.  Here  our  knowledge 
ends ;  the  mysterious  influence  of  matter  on  mind  will 
in  all  probability  be  forever  hid  from  man. 

A  series  of  experiments  by  Sir  John  Herschel  has 
disclosed  a  new  set  of  obscure  rays  hi  the  solar  spec- 
trum, which  seem  to  bear  the  same  relation  to  those  of 
heat  that  the  photographic  or  chemical  rays  bear  to  the 
luminous.  They  are  situate  in  that  part  of  the  spec- 
trum which  is  occupied  by  the  less  refrangible  visible 
colors,  and  have  been  named  by  their  discoverer  Parather- 
mic  rays.  It  must  be  held  in  remembrance  that  the 
region  of  greatest  heat  in  the  solar  spectrum  lies  in  the 
dark  space  beyond  the  visible  red.  Now  Sir  John  Her- 
schel found  that  in  experiments  with  a  solution  of  gum 
guaiacum  in  soda,  which  gives  the  paper  a  green  color, 
the  green,  yellow,  orange,  and  red  rays  of  the  spectrum 
invariably  discharged  the  color,  while  no  effect  was  pro- 
duced by  the  extra-spectral  rays  of  caloric,  which  ought 
to  have  had  the  greatest  effect,  had  heat  been  the  cause 
of  the  phenomenon.  When  an  aqueous  solution  of 
chlorine  was  poured  over  a  slip  of  paper  prepared  with 
gum  guaiacum  dissolved  in  soda,  a  color  varying  from  a 
deep  somewhat  greenish  hue  to  a  fine  celestial  blue  was 
given  to  it ;  and  when  the  solar  spectrum  was  thrown 
on  the  paper  while  moist,  the  color  was  discharged  from 
all  the  space  under  the  less  refrangible  luminous  rays, 
at  the  same  time  that  the  more  distant  thermic  rays 
beyond  the  spectrum  evaporated  the  moisture  from  the 
space  on  which  they  fell :  so  that  the  heat  spots  became 
apparent.  But  the  spots  disappeared  as  the  paper 
dried,  leaving  the  surface  unchanged ;  while  the  photo- 
graphic impression  within  the  visible  spectrum  increased 
in  intensity,  the  non-luminous  thermic  rays,  though 
evidently  active  as  to  heat,  were  yet  incapable  of  effect- 
ing that  peculiar  chemical  change  which  other  rays  of 
much  less  heating  power  were  all  the  time  producing. 
Sir  John  having  ascertained  that  an  artificial  heat  from 
180°  to  280°  of  Fahrenheit  changed  the  green  tint  of 


232  EXPERIMENTS  ON  LIGHT  AND  HEAT.  SECT.  XXV. 

gum  guaiacum  to  its  original  yellow  hue  when  moist, 
but  that  it  had  no  such  effect  when  dry,  he  therefore 
tried  whether  heat  from  a  hot  iron  applied  to  the  back 
of  the  paper  used  in  the  last-mentioned  experiment 
while  under  the  influence  of  the  solar  spectrum  might 
not  assist  the  action  of  the  calorific  rays  ;  but  instead  of 
doing  so,  it  greatly  accelerated  the  discoloration  over  the 
spaces  occupied  by  the  less  refrangible  rays,  but  had  no 
effect  on  the  extra-spectral  region  of  maximum  heat. 
Obscure  terrestrial  heat  therefore  is  capable  of  assisting 
and  being  assisted  in  effecting  this  peculiar  change  by 
those  rays  of  the  spectrum,  whether  luminous  or  ther- 
mic, which  occupy  its  red,  yellow,  and  green  regions, 
while  on  the  other  hand  it  receives  no  such  assistance 
from  the  purely  thermic  rays  beyond  the  spectrum 
acting  under  similar  circumstances  and  in  an  equal  state 
of  condensation. 

The  conclusions  drawn  from  these  experiments  are 
confirmed  by  that  which  follows :  a  photographic  picture 
formed  on  paper  prepared  with  a  mixture  of  the  solu- 
tions of  ammonia-citrate  of  iron  and  ferro-sesquicyanite 
of  potash  in  equal  parts,  then  thrown  into  water  and 
afterward  dried,  will  be  blue  and  negative,  that  is  to 
say,  the  lights  and  shadows  will  be  the  reverse  of  what 
they  are  in  nature.  If  in  this  state  the  paper  be  washed 
with  a  solution  of  proto-nitrate  of  mercury,  the  picture 
will  be  discharged :  but  if  it  be  well  washed  and  dried 
and  a  hot  smoothing  iron  passed  over  it,  the  picture  in- 
stantly reappears,  not  blue,  but  brown:  if  kept  some 
weeks  in  this  state  in  perfect  darkness  between  the 
leaves  of  a  portfolio,  it  fades  and  almost  entirely  vanishes, 
but  a  fresh  application  of  heat  restores  it  to  its  full  origi- 
nal intensity.  This  curious  change  is  not  the  effect  of 
light,  at  least  not  of  light  alone.  A  certain  temperature 
must  be  attained,  and  that  suffices  in  total  darkness  :  yet 
on  exposing  to  a  very  concentrated  spectrum  a  slip  of  the 
paper  used  in  the  last  experiment,  after  the  uniform 
blue  color  has  been  discharged  and  a  white  ground  left, 
this  whiteness  is  changed  to  brown  over  the  whole  re- 
gion of  the  red  and  orange  rays,  but  not  beyond  the 
luminous  spectrum. 

Sir  John  thence  concludes — 1st.  That  it  is  the  heat 


SKCT.  XXV.        CONCLUSIONS  TO  BE  DRAWN.  233 

of  these  rays,  not  their  light,  which  operates  the 
change ;  2dly.  That  this  heat  possesses  a  peculiar 
chemical  quality  which  is  not  possessed  by  the  purely 
calorific  rays  outside  of  the  visible  spectrum,  though  far 
more  intense ;  and,  3dly.  That  the  heat  radiated  from 
obscurely  hot  iron,  abounds  especially  in  rays  analogous 
to  those  of  the  region  of  the  spectrum  above  indicated. 

Another  instance  of  these  singular  transformations 
may  be  noticed.  The  pictures  formed  on  cyanotype 
paper,  rendered  more  sensitive  by  the  addition  of  cor- 
rosive sublimate,  are  blue  on  a  white  ground  and  posi- 
tive, that  is,  the  lights  and  shadows  are  the  same  as  in 
nature,  but  by  the  application  of  heat,  the  color  is 
changed  from  blue  to  brown,  from  positive  to  negative ; 
even  by  keeping  in  darkness  the  blue  color  is  restored, 
as  well  as  the  positive  character.  Sir  John  attributes 
this  as  in  the  former  instance  to  certain  rays,  which  re- 
garded as  rays  of  heat  or  light,  or  of  some  influence  sui 
generis  accompanying  the  red  and  orange  rays  of  the 
spectrum,  are  also  copiously  emitted  by  bodies  heated 
short  of  redness.  He  thinks  it  probable  that  these  in- 
visible parathermic  rays  are  the  rays  which  radiate 
from  molecule  to  molecule  in  the  interior  of  bodies,  that 
they  determine  the  discharge  of  vegetable  colors  at  the 
boiling  temperature,  and  also  the  innumerable  atomic 
transformations  of  organic  bodies  which  take  place  at 
the  temperature  below  redness,  that  they  are  distinct 
from'  those  of  pure  heat,  and  that  they  are  sufficiently 
identified  by  these  characters  to  become  legitimate  ob- 
jects of  scientific  discussion. 

The  calorific  and  parathermic  rays  appear  to  be  so 
intimately  connected  with  the  discoveries  of  Messrs. 
Draper  and  Moser  that  the  subject  of  solar  radiation 
would  be  imperfect  were  they  omitted.  The  dis- 
covery of  Daguerre  shows  that  the  action  of  light  on 
the  iodide  of  silver  renders  it  capable  of  condensing  the 
vapor  of  mercury  which  adheres  to  the  parts  affected 
by  it.  Professor  Moser  of  KOnigsberg  has  proved  that 
the  same  effect  is  produced  by  the  simple  contact  of 
bodies,  and  even  by  their  very  near  juxta-position,  and 
that  in  total  darkness  as  well  as  in  light.  This  dis- 
covery he  announced  in  the  following  words :  "  If  a 
u2 


234  DISCOVERIES  OF  PROFESSOR  MOSER.     SECT.  XXV. 

surface  has  been  touched  in  any  particular  parts  by  any 
body,  it  acquires  the  property  of  precipitating  all  va- 
pors, and  these  adhere  to  it  or  combine  chemically  with 
it  on  those  spots  differently  to  what  they  do  on  the  un- 
touched parts."  If  we  write  on  a  plate  of  glass  or  any 
smooth  surface  whatever  with  blotting  paper,  a  brush, 
or  anything  else,  and  then  clean  it,  the  characters  al- 
ways reappear  if  the  plate  or  surface  be  breathed  upon, 
and  the  same  effect  may  be  produced  even  on  the  sur- 
face of  mercury ;  nor  is  absolute  contact  necessary.  If 
a  screen  cut  in  a  pattern  be  held  over  a  polished  me- 
tallic surface  at  a  small  distance,  and  the  whole  breathed 
on :  after  the  vapor  has  evaporated  so  that  no  trace  is 
left  on  the  surface,  the  pattern  comes  out  when  it  is 
breathed  on  again. 

Professor  Moser  proved  that  bodies  exert  a  very  de- 
cided influence  upon  each  other,  by  placing  coins,  cut 
stones,  pieces  of  horn,  and  other  substances,  a  short 
time  on  a  warm  metallic  plate ;  when  the  substance 
was  removed  no  impression  appeared  on  the  plate  till  it 
was  breathed  upon  or  exposed  to  the  vapor  of  mercury, 
and  then  these  vapors  adhered  only  to  the  parts  where 
the  substance  had  been  placed,  making  distinct  images, 
which  in  some  cases  were  permanent  after  the  vapor 
was  removed.  Similar  impressions  were  obtained  on 
glass  and  other  substances  even  when  the  bodies  were 
not  in  contact,  and  the  results  were  the  same  whether 
the  experiments  were  performed  in  light  or  in  darkness. 

Mr.  Hunt  has  shown  that  many  of  these  phenomena 
depend  on  difference  of  temperature,  and  that  in  order 
to  obtain  good  impressions  dissimilar  metals  must  be 
used.  For  example,  gold,  silver,  bronze,  and  copper 
coins  were  placed  on  a  plate  of  copper  too  hot  to  be 
touched,  and  allowed  to  remain  till  the  plate  cooled ; 
all  the  coins  had  made  an  impression,  the  distinctness 
and  intensity  of  which  was  in  the  order  of  the  metals 
named.  When  the  plate  was  exposed  to  the  vapor  of 
mercury  the  result  was  the  same,  but  when  the  vapor 
was  wiped  off,  the  gold  and  silver  coins  only  had  left 
permanent  images  on  the  copper.  These  impressions 
are  often  minutely  perfect  whether  the  coins  are  in 
actual  contact  with  the  plate  or  £  of  an  inch  above  it. 


SECT.  XXV.  LATENT  CALORIC.  235 

The  mass  of  the  metal  has  a  material  influence  on  the 
result ;  a  large  copper  coin  makes  a  better  impression 
on  a  copper  plate  than  a  small  silver  coin.  When  coins 
of  different  metals  are  placed  on  the  same  -plate  they 
interfere  with  each  other. 

When,  instead  of  being  heated,  the  copper  plate 
was  cooled  by  a  freezing  mixture,  and  bad  conductors  of 
heat  laid  upon  it,  as  wood,  paper,  glass,  &c.,  the  result 
was  similar,  showing  that  the  phenomena  could  be  pro- 
duced by  any  disturbance  of  the  caloric  latent  in  the 
substances. 

There  can  be  no  doubt  that  these  phenomena  are 
universal,  since  all  substances  are  more  or  less  sensitive 
to  light,  which  must  produce  innumerable  changes  in 
the  nature  of  terrestrial  things,  especially  in  the  vege- 
table tribe,  by  the  power  it  gives  of  condensing  vapor 
and  consequently  the  deposition  of  dew. 

Red  and  orange-colored  media,  smoked  glass,  and  all 
bodies  that  transmit  or  absorb  the  calorific  rays  freely, 
leave  strong  impressions  on  a  plate  ef  copper  whether 
they  be  in  contact  or  |  of  an  inch  above  the  plate.  The 
strongest  proof  that  heat  is  concerned  in  some  at  least 
of  these  phenomena  is  evident.  For  instance,  a  solar 
spectrum  concentrated  by  a  lens  was  thrown  on  a  pol- 
ished plate  of  copper  and  kept  on  the  same  spot  by  a 
heliostat  for  one,  two,  or  three  hours ;  when  exposed 
to  mercurial  vapor  a  film  of  the  vapor  covered  the  plate 
where  the  diffused  light  which  always  accompanies  the 
solar  spectrum  had  fallen ;  on  the  obscure  space  occu- 
pied by  the  maximum  heating  power  of  Sir  William 
Herschel,  and  also  the  great  heat  spot  in  the  thermic 
spectrum  of  Sir  John  Herschel,  the  condensation  of  the 
mercury  was  so  thick  that  it  stood  out  a  distinct  white 
spot  on  the  plate,  while  over  the  whole  space  that  had 
been  under  the  visible  spectrum  the  quantity  of  vapor 
was  much  less  than  that  which  covered  the  other  parts, 
affording  distinct  evidence  of  a  negative  effect  hi  the 
luminous  spectrum,  and  of  the  power  of  the  calorific 
rays,  which  is  not  always  confined  to  the  surface  of  the 
metal,  since  in  many  instances  the  impressions  are  formed 
to  a  considerable  depth  below  it,  and  consequently  are 
permanent. 


236  THE  ART  OP  THERMOGRAPHY.        SECT.  XXV. 

Mr.  Hunt  observing  that  a  black  substance  leaves  a 
stronger  impression  on  a  metallic  surface  than  a  white, 
applied  the  property  to  the  art  of  thermography,  by 
which  he  copies  prints,  wood-cuts,  writing,  and  printing, 
on  copper  amalgamated  on  one  surface  and  highly  pol- 
ished, merely  by  placing  the  object  to  be  copied 
smoothly  on  the  metal  and  pressing  it  into  close  contact 
by  a  plate  of  glass :  after  some  hours  the  plate  is  sub- 
j  ected  to  the  vapor  of  mercury  and  afterward  t6  that  of 
iodine,  when  a  black  and  accurate  impression  of  the 
object  comes  out  on  a  gray  ground.  Effects  similar  to 
those  attributed  to  heat  may  also  be  produced  by  elec- 
tricity :  Mr.  Karsten,  by  placing  a  glass  plate  upon  one 
of  metal,  and  on  the  glass  plate  a  medal  subjected  to 
discharges  of  electricity,  found  a  perfect  image  of  the 
medal  impressed  on  the  glass,  which  could  be  brought 
into  evidence  by  either  mercury  or  iodine  ;  and  when 
several  plates  of  glass  were  interposed  between  the 
medal  and  the  metallic  plate,  each  plate  of  glass  re- 
ceived an  image  on  its  upper  surface  after  the  passage 
of  electrical  discharges.  These  discharges  have  the 
remarkable  power  of  restoring  impressions  that  have 
been  long  obliterated  from  plates  by  polishing ;  a  proof 
that  the  disturbances  upon  which  these  phenomena 
depend  are  not  confined  to  the  surface  of  the  metals, 
but  that  a  very  decided  molecular  change  has  taken 
place  to  a  considerable  depth.  Mr.  Hunt's  experiments 
prove  that  the  electro-negative  metals  make  the  most 
decided  images  upon  electro-negative  plates,  and  vice 
versa.  M.  Matteucci  has  shown  that  a  discharge  of 
electricity  does  not  visibly  affect  a  polished  silver  plate, 
but  that  it  produces  an  alteration  which  renders  it  capa- 
ble of  condensing  vapor. 

M.  Fizean  ascribes  a  numerous  class  of  these  phe- 
nomena to  the  action  of  a  slight  layer  of  organic  or  fatty 
matter  on  the  surfaces,  which,  being  volatile,  is  trans- 
ferred to  any  body  near,  in  a  greater  or  less  quantity  ac- 
cording to  the  distance  ;  that  is,  according  as  the  sur- 
face projects  or  sinks  into  hollows.  When  the  different 
parts  of  a  surface  are  unequally  soiled  by  extraneous 
bodies,  even  in  the  minutest  quantity,  the  condensation 
of  mercurial  vapor  is  effected  in  a  manner  visibly  dif- 


SECT.  XXV.    VARIOUS  PHENOMENA  EXPLAINED.  237 

ferent  on  its  different  parts,  and  therefore  images  are 
formed.  Although  this  explains  various  phenomena,  it 
does  not  apply  to  those  already  described,  as  Mr.  Hunt 
had  taken  the  precaution  to  divest  the  substances  he 
used  of  every  trace  of  organic  matter. 

It  is  difficult  to  see  to  what  cause  Mr.  Hunt's  experi- 
ments on  the  reciprocal  action  of  bodies  in  total  darkness 
can  be  attributed,  unless  perhaps  to  a  constant  radiation 
of  some  peculiar  principle  from  their  surfaces,  which 
really  seems  to  exist. 

The  impression  of  an  engraving  was  made  by  laying 
it  face  downwards  on  a  silver  plate  iodized,  and  placing 
an  amalgamated  copper  plate  upon  it :  it  was  left  hi 
darkness  fifteen  hours,  when  an  impression  of  the  en- 
graving had  been  made  on  the  amalgamated  plate, 
through  the  paper. 

As  the  same  may  be  obtained  on  plates  of  iron,  zinc, 
or  lead,  it  is  evident  that  this  result  is  not  the  effect  of 
chemical  rays. 

An  iodized  silver  plate  was  placed  in  darkness  with  a 
coil  of  string  laid  on  it,  and  with  a  polished  silver  plate 
suspended  one  eighth  of  an  inch  above  it ;  after  four 
hours  they  were  exposed  to  the  vapors  of  mercury, 
which  became  uniformly  deposited  on  the  iodized  plate, 
but  on  the  silver  one  there  Was  a  sharp  image  of  the 
string,  so  that  this  image  was  formed  in  the  dark,  and 
even  without  contact.  Coins  or  other  objects  leave 
their  impressions  in  the  same  manner  with  perfect 
sharpness  and  accuracy,  when  brought  out  by  vapor 
without  contact,  in  darkness,  and  on  simple  metals. 

Heat,  electricity,  and  the  evaporation  of  unctuous 
matter,  may  account  for  some  of  these  phenomena,  but 
Qthers  clearly  point  at  some  unknown  influence  exerted 
between  the  surfaces  of  solid  bodies,  and  affecting  their 
molecular  structure  so  as  to  determine  the  precipitation 
of  vapors,  an  influence  which  in  all  probability  will  ulti- 
mately be  found  to  be  either  the  parathermic  rays  of 
Sir  John  Herschel,  or  ultimately  connected  with  them. 


238  ATMOSPHERE  OF  THE  MOON.         JECT.  XXVL 


SECTION  XXVI. 

Atmosphere  of  the  Planets  and  the  Moon— Constitution  of  the  Sun— Esti- 
mation of  the  Sun's  tight — His  Influence  on  the  different  Planets — 
Temperature  of  Space  —Internal  Heat  of  the  Earth — Zone  of  Constant 
Temperature — Heat  increases  with  the  Depth— Heat  in  Mines  and 
Wells— Thermal  Springs— Central  Heat— Volcanic  Action— The  Heat 
above  the  Zone  of  Constant  Temperature  entirely  from  the  Sun — The 
Quantity  of  Heat  annually  received  from  the  Sun— Isogeothermal  Lines 
— Distribution  of  Heat  on  the  Earth — Climate — Line  of  Perpetual  Con- 
gelation— Causes  affecting  Climate— Isothermal  Lines — Excessive  Cli- 
mates— The  same  Quantity  of  Heat  annually  received  and  radiated  by 
the  Earth. 

THE  ocean  of  light  and  heat  perpetually  flowing  from 
the  sun,  must  affect  the  bodies  of  the  system  very  differ- 
ently, on  account  of  the  varieties  in  their  atmospheres, 
some  of  which  appear  to  be  very  extensive  and  dense. 
According  to  the  observations  of  Schroeter,  the  atmos- 
phere of  Ceres  is  more  than  668  miles  high,  and  that  of 
Pallas  has  an  elevation  of  465  miles.  These  must  re- 
fract the  light  and  prevent  the  radiation  of  heat  like  our 
own.  But  it  is  remarkable  that  not  a  trace  of  atmosphere 
can  be  perceived  in  Vesta.  The  action  of  the  sun's  rays 
must  be  very  different  on  such  bodies  from  what  it  is 
on  the  earth,  and  the  heat  imparted  to  them  quickly 
lost  by  radiation ;  yet  it  is  impossible  to  estimate  their 
temperature,  since  the  cold  may  be  counteracted  by 
their  central  heat,  if,  as  there  is  reason  to  presume,  they 
have  originally  been  in  a  state  of  fusion,  possibly  of 
vapor.  The  attraction  of  the  earth  has  probably  de- 
prived the  moon  of  hers ;  for  the  refractive  power  of 
the  air  at  the  surface  of  the  earth  is  at  least  a  thousand 
times  as  great  as  refraction  at  the  surface  of  the  moon. 
The  lunar  atmosphere,  therefore,  must  be  of  a  greater 
degree  of  rarity  than  can  be  produced  by  our  best  air- 
pumps  ;  consequently  no  terrestrial  animal  could  exist 
in  it.  This  was  confirmed  by  M.  Arago's  observations 
during  the  last  great  solar  eclipse,  when  no  trace  of  a 
lunar  atmosphere  was  to  be  seen. 

The  sun  has  a  very  dense  atmosphere,  which  is 
probably  the  cause  of  the  peculiar  phenomena  in  his 
photographic  image  already  mentioned.  What  his  body 
may  be,  it  is  impossible  to  conjecture  ;  but  he  seems  to 


SECT.  XXVI.        CONSTITUTION  OF  THE  SUN.  239 

be  surrounded  by  a  mottled  ocean  of  flame,  through 
which  his  dark  nucleus  appears  like  black  spots  often  of 
enormous  size.  These  spots  are  almost  always  com- 
prised within  a  zone  of  the  sun's  surface,  whose  breadth, 
measured  on  a  solar  meridian,  does  not  extend  beyond  30$° 
on  each  side  of  his  equator,  though  they  have  been  seen 
at  the  distance  of  39i°.  From  their  extensive  and  rapid 
changes,  there  is  every  reason  to  suppose  that  the  exte- 
rior and  incandescent  part  of  the  sun  is  gaseous.  The 
solar  rays,  probably  arising  from  chemical  processes  that 
continually  take  place  at  his  surface,  or  from  electricity, 
are  transmitted  through  space  in  all  directions ;  but  not- 
withstanding the  sun's  magnitude,  and  the  inconceivable 
heat  that  must  exist  at  his  surface,  as  the  intensity  both 
of  his  light  and  heat  diminishes  as  the  square  of  the  dis- 
tance increases,  his  kindly  influence  can  hardly  be  felt 
at  the  boundaries  of  our  system,  or  at  all  events  it  must 
be  but  feeble. 

The  direct  light  of  the  sun  has  been  estimated  to  be 
equal  to  that  of  5563  wax  candles  of  moderate  size,  sup- 
posed to  be  placed  at  the  distance  of  one  foot  from  the 
object.  That  of  the  moon  is  probably  only  equal  to  the 
light  of  one  candle  at  the  distance  of  twelve  feet.  Con- 
sequently the  light  of  the  sun  is  more  than  three  hundred 
thousand  times  greater  than  that  of  the  moon.  Hence 
the  light  of  the  moon  imparts  no  heat.  Professor  Forbes 
is  convinced  by  recent  experiments  that  the  direct  light 
of  the  moon  is  incapable  of  raising  a  thermometer  one 
three-hundred-thousandth  part  of  a  centigrade  degree, 
at  least  in  this  climate.  The  intensity  of  the  sun's  light 
diminishes  from  the  center  to  the  circumference  of  the 
solar  disc. 

In  Uranus,  the  sun  must  be  seen  like  a  small  but  bril- 
liant star,  not  above  the  hundred  and  fiftieth  part  so 
bright  as  he  appears  to  us ;  but  that  is  2000  times  brighter 
than  our  moon ;  so  that  he  is  really  a  sun  to  Uranus, 
and  may  impart  some  degree  of  warmth.  But  if  we 
consider  that  water  would  not  remain  fluid  in  any  part 
of  Mars,  even  at  his  equator,  and  that  in  the  temperate 
zones  of  the  same  planet  even  alcohol  and  quicksilver 
would  freeze,  we  may  form  some  idea  of  the  cold  that 
must  reign  in  Uranus. 


240  TEMPERATURE  OF  SPACE.  SECT.  XXVI. 

The  climate  of  Venus  more  nearly  resembles  that  of 
the  earth,  though,  excepting  perhaps  at  her  poles,  much 
too  hot  for  animal  and  vegetable  life  as  they  exist  here ; 
but  in  Mercury,  the  mean  heat  arising  only  from  the 
intensity  of  the  sun's  rays  must  be  above  that  of  boiling 
quicksilver,  and  water  would  boil  even  at  his  poles. 
Thus  the  planets,  though  kindred  with  the  earth  in  mo- 
tion and  structure,  are  totally  unfit  for  the  habitation  of 
such  a  being  as  man,  unless,  indeed,  their  temperature 
should  be  modified  by  circumstances  of  which  we  are 
not  aware,  and  which  may  increase  or  diminish  the 
sensible  heat  so  as  to  render  them  habitable. 

It  is  found  by  experience,  that  heat  is  developed  in 
opaque  and  translucent  substances  by  their  absorption  of 
solar  light,  but  that  the  sun's  rays  do  not  sensibly  alter 
the  temperature  of  perfectly  transparent  bodies  through 
which  they  pass.  As  the  temperature  of  the  pellucid 
planetary  space  can  be  but  little  affected  by  the  passage 
of  the  sun's  light  and  heat,  neither  can  it  be  sensibly 
raised  by  die  heat  now  radiated  from  the  earth ;  conse- 
quently its  temperature  must  be  invariable,  at  least 
throughout  the  extent  of  the  solar  system.  The  at- 
mosphere, on  the  contrary,  gradually  increasing  in  den- 
sity toward  the  surface  of  the  earth,  becomes  less  pel- 
lucid, and  therefore  gradually  increases  in  temperature, 
both  from  the  direct  action  of  the  sun,  and  from  the  ra- 
diation of  the  earth.  Lambert  had  proved  that  the  ca- 
pacity of  the  atmosphere  for  heat  varies  according  to  the 
same  law  with  its  capacity  for  absorbing  a  ray  of  light 
passing  through  it  from  the  zenith,  whence  M.  Svanberg 
found  that  the  temperature  of  space  is  58°  below  the 
zero  point  of  Fahrenheit's  thermometer.  From  other 
researches,  founded  upon  the  rate  and  quantity  of  at- 
mospheric refraction,  he  obtained  a  result  which  only 
differs  from  the  preceding  by  half  a  degree.  M.  Fourier 
has  arrived  at  nearly  the  same  conclusion  from  the  law 
of  the  radiation  of  the  heat  of  the  terrestrial  spheroid, 
on  the  hypothesis  of  its  having  nearly  attained  its  limit 
of  temperature  in  cooling  down  from  its  supposed  prim- 
itive state  of  fusion.  The  difference  in  the  result  of 
these  three  methods,  totally  independent  of  one  another, 
only  amounts  to  the  fraction  of  a  degree. 


SKOT.  XXVI.    INTERNAL  HEAT  OF  THE  EARTH.  241 

The  cold  endured  by  Sir  Edward  Parry  one  day  in 
Melville  Island  was  55°  below  zero ;  and  that  suffered 
by  Captain  Back  on  the  17th  of  January,  1834,  in  62° 
46^'  of  north  latitude,  was  no  less  than  70°  below  the 
same  point.  However,  M.  Poisson  attributes  this  to  ac- 
cidental circumstances,  and  by  a  recent  computation,  he 
makes  the  temperature  of  space  to  be  8°  above  the  zero 
of  Fahrenheit.  This  he  considers  greatly  to  exceed  the 
temperature  of  the  exterior  strata  of  the  atmosphere, 
which  he  conceives  to  be  deprived  of  their  elasticity  by 
intense  cold,  and  he  thus  accounts  for  the  decrease  of 
temperature  at  great  elevations,  and  for  the  limited  ex- 
tent of  the  atmosphere. 

Doubtless,  the  radiation  of  all  the  bodies  in  the  uni- 
verse maintains  the  ethereal  medium  at  a  higher  tem- 
perature than  it  would  otherwise  have,  and  must  event- 
ually increase  it,  but  by  a  quantity  so  evanescent  that  it 
is  hardly  possible  to  conceive  a  time  when  a  change  will 
become  perceptible. 

The  temperature  of  space  being  so  low,  it  becomes  a 
matter  of  no  small  interest  to  ascertain  whether  the  earth 
may  not  be  ultimately  reduced  by  radiation  to  the  tem- 
perature of  the  surrounding  medium ;  what  the  sources 
of  heat  are ;  and  whether  they  be  sufficient  to  compen- 
sate the  loss,  and  to  maintain  the  earth  in  a  state  fit  for 
the  support  of  animal  and  vegetable  life  in  time  to  come. 
All  observations  that  have  been  made  under  the  surface 
of  the  ground  concur  in  proving  that  there  is  a  stratum 
at  the  depth  of  from  40  to  100  feet  throughout  the  whole 
earth,  where  the  temperature  is  invariable  at  all  times 
and  seasons,  and  which  differs  but  little  from  the  mean 
annual  temperature  of  the  country  above.  According  to 
M.  Boussingault,  indeed,  that  stratum  at  the  equator  is 
at  the  depth  of  little  more  than  a  foot  in  places  sheltered 
from  the  direct  rays  of  the  sun ;  but  in  our  climates  it 
is  at  a  much  greater  depth.  In  the  course  of  more  than 
half  a  century,  the  temperature  of  the  earth  at  the 
depth  of  90  feet  in  the  caves  of  the  Observatory  at  Paris 
has  never  been  above  or  below  53°  of  Fahrenheit's  ther- 
mometer, which  is  only  2°  above  the  mean  annual  tem- 
perature at  Paris.  This  zone,  unaffected  by  the  sun's 
rays  from  above,  or  by  the  internal  heat  from  below, 
16  X 


242  HEAT  IN  MINES  AND  WELLS.        SECT.  XXVI. 

serves  as  an  origin  whence  the  effects  of  the  external 
heat  are  estimated  on  one  side,  and  the  internal  temper- 
ature of  the  globe  on  the  other. 

As  early  as  the  year  1740,  M.  Gensanne  discovered 
in  the  lead  mines  of  Geromagny,  three  leagues  from 
Befort,  that  the  heat  of  the  ground  increases  with  the 
depth  below  the  zone  of  constant  temperature.  A  vast 
number  of  observations  have  been  made  since  that  time 
in  the  mines  of  Europe  and  America,  by  MM.  Saussure, 
Daubuisson,  Humboldt,  Cordier,  Fox,  Reich,  and  others, 
which  agree,  without  an  exception,  in  proving  that  the 
temperature  of  the  earth  becomes  higher  in  descending 
toward  its  center.  The  greatest  depth  that  has  been 
attained  is  in  the  silver  mine  of  Guamaxato  in  Mexico, 
where  M.  de  Humboldt  found  a  temperature  of  98°  at 
the  depth  of  285  fathoms  ;  the  mean  annual  temperature 
of  the  country  being  only  61°.  Next  to  that  is  the  Dal- 
coath  copper  mine  in  Cornwall,  where  Mr.  Fox's  ther- 
mometer stood  at  68°  in  a  hole  in  the  rock  at  the  depth 
of  230  fathoms,  and  at  82°  in  water  at  the  depth  of  240 
fathoms,  the  mean  annual  temperature  at  the  surface 
being  about  50°.  But  it  is  needless  to  multiply  exam- 
ples, all  of  which  concur  in  showing  that  there  is  a  very 
great  difference  between  the  temperature  in  the  interior 
of  the  earth  and  at  its  surface.  Mr.  Fox's  observations 
on  the  temperature  of  springs  which  rise  at  profound 
depths  in  mines,  afford  the  strongest  testimony.  He 
found  considerable  streams  flowing  into  some  of  the 
Cornish  mines  at  the  temperature  of  80°  or  90°,  which 
is  about  30°  or  40°  above  that  of  the  surface;  and  also 
ascertained  that  nearly  2,000,000  gallons  of  water  are 
daily  pumped  from  the  bottom  of  the  Poldice  mine, 
which  is  176  fathoms  deep,  at  90°  or  100°.  As  this  is 
higher  than  the  warmth  of  the  human  body,  Mr.  Fox 
justly  observes  that  it  amounts  to  a  proof  that  the  in- 
creased temperature  cannot  proceed  from  the  persons  of 
the  workmen  employed  in  the  mines.  Neither  can  the 
warmth  of  mines  be  attributed  to  the  condensation  of 
the  currents  of  air  which  ventilate  them.  Mr.  Fox, 
whose  opinion  is  of  high  authority  in  these  matters, 
states  that  even  in  the  deepest  mines,  the  condensation 
of  the  air  would  not  raise  the  temperature  more  than 


.  XXVI.        HEAT  IN  MINES  AND  WELLS.  243 

5°  or  6°,  and  that  if  the  heat  could  be  attributed  to  this 
cause,  the  seasons  would  sensibly  affect  the  temperature 
of  mines,  which  it  appears  they  do  not  where  the  deptk 
is  great.  Besides,  the  Cornish  mines  are  generally 
ventilated  by  numerous  shafts  opening  into  the  galleries 
from  the  surface  or  from  a  higher  level.  The  air  circu- 
lates freely  in  these,  descending  in  some  shafts  and  as- 
cending in  others.  In  all  cases,  Mr.  Fox  found  that  the 
upward  currents  are  of  a  higher  temperature  than  the 
descending  currents ;  so  much  so,  that  in  winter  the 
moisture  is  often  frozen  in  the  latter  to  a  considerable 
depth ;  the  circulation  of  air,  therefore,  tends  to  cool 
the  mine  instead  of  increasing  the  heat.  Mr.  Fox  has 
also  removed  the  objections  arising  from  the  compara- 
tively low  temperature  of  the  water  in  the  shafts  of 
abandoned  mines,  by  showing  that  observations  in  them, 
from  a  variety  of  circumstances  which  he  enumerates, 
are  too  discordant  to  furnish  any  conclusion  as  to  the 
actual  heat  of  the  earth.  The  high  temperature  of 
mines  might  be  attributed  to  the  effects  of  the  fires, 
candles,  and  gunpowder  used  by  the  miners,  did  not  a 
similar  increase  obtain  in  deep  wells,  and  in  borings  to 
great  depths  in  search  of  water,  where  no  such  causes 
of  disturbance  occur.  In  a  well  dug  with  a  view  to 
discover  salt  in  the  canton  of  Berne,  and  long  deserted, 
M.  de  Saussure  had  the  most  complete  evidence  of  in- 
creasing heat.  The  same  has  been  confirmed  by  the 
temperature  of  many  wells,  both  in  France  and  England, 
especially  by  the  Artesian  wells,  so  named  from  a  pecu- 
liar method  of  raising  water  first  resorted  to  in  Artois, 
and  since  become  very  general.  An  Artesian  well  con- 
sists of  a  shaft  of  a  few  inches  in  diameter,  bored  into 
the  earth  till  a  spring  is  found.  To  prevent  the  water 
being  earned  off  by  the  adjacent  strata,  a  tube  is  let 
down  which  exactly  fills  the  bore  from  top  to  bottom,  in 
which  the  water  rises  pure  to  the  surface.  It  is  clear 
the  water  could  not  rise  unless  it  had  previously  de- 
scended from  high  ground  through  the  interior  of  the 
earth  to  the  bottom  of  the  well.  It  partakes  of  the 
temperature  of  the  strata  through  which  it  passes,  and 
in  every  instance  has  been  warmer  in  proportion  to  the 
depth  of  the  well ;  but  it  is  evident  that  the  law  of  in- 


244  THERMAL  SPRINGS.  SKCT.  XXVI. 

crease  cannot  be  obtained  in  this  manner.  Perhaps  the 
most  satisfactory  experiments  on  record  are  those  made 
by  MM.  August  de  la  Rive  and  F.  Marcet  during  the 
year  1833,  in  a  boring  for  water  about  a  league  from 
Geneva,  at  a  place  318  feet  above  the  level  of  the  lake. 
The  depth  of  the  bore  was  727  feet,  and  the  diameter 
only  between  four  and  five  inches.  No  spring  was  ever 
found  ;  but  the  shaft  filled  with  mud,  from  the  moisture 
of  the  ground  mixing  with  the  earth  displaced  in  boring, 
which  was  peculiarly  favorable  for  the  experiments,  as 
the  temperature  at  each  depth  may  be  considered  to  be 
that  of  the  particular  stratum.  In  this  case,  where  none 
of  the  ordinary  causes  of  disturbance  could  exist,  and 
where  every  precaution  was  employed  by  scientific  and 
experienced  observers,  the  temperature  was  found  to 
increase  regularly  and  uniformly  with  the  depth  at  the 
rate  of  about  1°  of  Fahrenheit  for  every  52  feet.  Pro- 
fessor Reich  of  Freyberg  has  found  that  the  mean  of  a 
great  number  of  observations  both  in  mines  and  wells  is 
1°  of  Fahrenheit  for  every  55  feet  of  depth,  and  from 
M.  Arago's  observations  in  an  Artesian  well  now  boring 
in  Paris,  the  increase  is  1°  of  Fahrenheit  for  every  45 
feet.  Though  there  can  be  no  doubt  as  to  the  increase 
of  temperature  in  penetrating  the  crust  of  the  earth, 
there  is  still  much  uncertainty  as  to  the  law  of  increase, 
which  varies  with  the  nature  of  the  soil  and  other  local 
circumstances  ;  but  on  an  average,  it  has  been  estimated 
at  the  rate  of  1°  for  eveiy  50  or  60  feet,  which  corre- 
sponds with  the  observations  of  MM.  Marcet  and  de  la 
Rive.  In  consequence  of  the  rapid  increase  of  internal 
heat,  thermal  springs,  or  such  as  are  independent  of 
volcanic  action,  rising  from  a  great  depth,  must  neces- 
sarily be  very  rare  and  of  a  high  temperature,  and  it  is 
actually  found  that  none  are  so  low  as  68°  of  Fahren- 
heit :  that  of  Chaudes  Aigues  in  Auvergne  is  about 
136°.  In  many  places  warm  water  from  Artesian  wells 
will  probably  come  into  use  for  domestic  purposes,  and 
it  is  even  now  employed  in  manufactories  at  Wurtem- 
berg,  in  Alsace,  and  near  Stutgardt. 

It  is  hardly  to  be  expected  that  at  present  any  infor- 
mation with  regard  to  the  actual  internal  temperature 
of  the  earth  should  be  obtained  from  that  of  the  ocean, 


SECT.  XXVI.      CENTRAL  HEAT  OP  THE  EARTH.  245 

on  account  of  the  mobility  of  fluids,  by  which  the  colder 
masses  sink  downward,  while  those  that  are  warmer 
rise  to  the  surface.  Nevertheless  it  may  be  stated,  that 
the  temperature  of  the  sea  decreases  with  the  depth 
between  the  tropics ;  while  on  the  contrary,  all  our 
northern  navigators  found  that  the  temperature  increases 
with  the  depth  in  the  polar  seas.  The  change  takes 
place  about  the  70th  parallel  of  latitude.  Some  ages 
hence,  however,  it  may  be  known  whether  the  earth 
has  arrived  at  a  permanent  state  as  to  heat,  by  comparing 
secular  observations  of  the  temperature  of  the  ocean  if 
made  at  a  great  distance  from  the  land. 

Should  the  earth's  temperature  increase  at  the  rate 
of  1°  for  every  fifty  feet,  it  is  clear  that  at  the  depth  of 
200  miles  the  hardest  substances  must  be  in  a  state  of 
fusion,  and  our  globe  must  in  that  case  either  be  encom- 
passed by  a  stratum  of  melted  lava  at  that  depth,  or  it 
must  be  a  ball  of  liquid  fire  7600  miles  in  diameter,  in- 
closed in  a  thin  coating  of  solid  matter ;  for  200  miles 
are  nothing  when  compared  with  the  size  of  the  earth. 
No  doubt  the  form  of  the  earth,  as  determined  by  the 
pendulum  and  arcs  of  the  meridian,  as  well  as  by  the 
motions  of  the  moon,  indicates  original  fluidity  and  subse- 
quent consolidation  and  reduction  of  temperature  by  ra- 
diation ;  but  whether  the  law  of  increasing  temperature 
is  uniform  at  still  greater  depths  than  those  already 
attained  by  man,  it  is  impossible  to  say.  At  all  events, 
internal  fluidity  is  not  inconsistent  with  the  present 
state  of  the  earth's  surface,  since  earthy  matter  is  as 
bad  a  conductor  of  caloric  as  lava,  which  often  retains 
its  heat  at  a  very  little  depth  for  years  after  its  surface 
is  cool.  Whatever  the  radiation  of  the  earth  might 
have  been  in  former  times,  certain  it  is  that  it  goes  on 
very  slowly  in  our  days ;  for  M.  Fourier  has  computed 
that  the  central  heat  is  decreasing  from  radiation  by 
only  about  the  j^^th  part  of  a  second  in  a  century.  If 
so,  there  can  be  no  doubt  that  it  will  ultimately  be  dis- 
sipated ;  but  as  far  as  regards  animal  and  vegetable  life, 
it  is  of  very  little  consequence  whether  the  center  of 
our  planet  be  liquid  fire  or  ice,  since  its  condition  in 
either  case  could  have  no  sensible  effect  on  the  climate  at 
its  surface.  The  internal  fire  does  not  even  impart  heat 
x2 


246  VOLCANIC  ACTION.  SECT.  XXVI. 

enough  to  melt  the  snow  at  the  poles,  though  so  much 
nearer  to  the  center  than  any  other  part  of  the  globe. 

The  immense  extent  of  active  volcanic  fire  is  one  of 
the  causes  of  heat  which  must  not  be  overlooked. 

The  range  of  the  Andes  from  Chili  to  the  north  of 
Mexico,  probably  from  Cape  Horn  to  California,  or  even 
to  New  Madrid  in  the  United  States,  is  one  vast  district 
of  igneous  action,  including  the  Caribbean  Sea  and  the 
West  Indian  Islands  on  one  hand  ;  and  stretching  quite 
across  the  Pacific  Ocean,  through  the  Polynesian  Archi- 
pelago, the  New  Hebrides,  the  Georgian  and  Friendly 
Islands,  on  the  other.  Another  chain  begins  with  the 
Aleutian  Islands,  extends  to  Kamtschatka,  and  from 
thence  passes  through  the  Kurile,  Japanese,  and  Phil- 
ippine Islands,  to  the  Moluccas,  whence  it  spreads  with 
terrific  violence  through  the  Indian  Archipelago,  even 
to  the  Bay  of  Bengal.  Volcanic  action  may  again  be 
followed  from  the  entrance  of  the  Persian  Gulf  to  Mad- 
agascar, Bourbon,  the  Canaries,  and  Azores.  Thence 
a  continuous  igneous  region  extends  through  about  1000 
geographical  miles  to  the  Caspian  Sea,  including  the 
Mediterranean,  and  extending  north  and  south  between 
the  35th  and  40th  parallels  of  latitude ;  and  in  central 
Asia  a  volcanic  region  occupies  2500  square  geographical 
miles.  The  volcanic  fires  are  developed  in  Iceland  in 
tremendous  force ;  and  the  antarctic  land  recently  dis- 
covered by  Sir  James  Ross  is  an  igneous  formation  of 
the  boldest  structure,  from  whence  a  volcano  in  high 
activity  rises  12,000  feet  above  the  perpetual  ice  of 
these  polar  deserts,  and  within  19£°  of  the  south  pole. 
Throughout  this  vast  portion  of  the  world  the  subterra- 
neous fire  is  often  intensely  active,  producing  such  vio- 
lent earthquakes  and  eruptions  that  their  effects,  accu- 
mulated during  millions  of  years,  may  account  for  many 
of  the  great  geological  changes  of  igneous  origin  that 
have  already  taken  place  in  the  earth,  and  may  occasion 
others  not  less  remarkable,  should  time — that  essential 
element  in  the  vicissitudes  of  the  globe — be  granted,  and 
their  energy  last. 

Mr.  Lyell,  who  has  shown  the  power  of  existing  causes 
with  great  ingenuity,  estimates  that  on  an  average  twenty 
eruptions  take  place  annually  in  different  parts  of  tho 


SECT.  XX VI.  VOLCANIC  ERUPTTONS.  247 

world ;  and  many  must  occur  or  have  happened,  even  on 
the  most  extensive  and  awful  scale,  among  people  equally 
incapable  of  estimating  their  effects  and  of  recording 
them.  We  should  never  have  known  the  extent  of  the 
fearful  eruption  which  took  place  in  the  island  of  Sum- 
bawa,  in  1815,  but  for  the  accident  of  Sir  Stamford  Raf- 
fles having  been  governor  of  Java  at  the  time.  It  began 
on  the  5th  of  April,  and  did  not  entirely  cease  till  July. 
The  ground  was  shaken  through  an  area  of  1000  miles 
in  circumference ;  the  tremors  were  felt  in  Java,  the 
Moluccas,  a  great  part  of  Celebes,  Sumatra,  and  Borneo. 
The  detonations  were  heard  in  Sumatra,  at  the  distance 
of  970  geographical  miles  in  a  straight  line ;  and  at  Ter- 
nate,  720  miles  in  the  opposite  direction.  The  most 
dreadful  whirlwinds  carried  men  and  cattle  into  the  ah* ; 
and  with  the  exception  of  26  persons,  the  whole  popu- 
lation of  the  island  perished  to  the  amount  of  12,000. 
Ashes  were  carried  300  miles  to  Java,  in  such  quantities 
that  the.  darkness  during  the  day  was  more  profound 
than  ever  had  been  witnessed  in  the  most  obscure  night. 
The  face  of  the  country  was  changed  by  the  streams  of 
lava,  and  by  the  upheaving  and  sinking  of  the  soil.  The 
town  of  Tomboro  was  submerged,  and  water  stood  to 
the  depth  of  18  feet  in  places  which  had  been  dry  land. 
Ships  grounded  where  they  had  previously  anchored, 
and  others  could  hardly  penetrate  the  mass  of  cinders 
which  floated  on  the  surface  of  the  sea  for  several  miles 
to  the  depth  of  two  feet.  A  catastrophe  similar  to  this, 
though  of  less  magnitude,  took  place  in  the  island  of  Bali 
in  1808,  which  was  not  heard  of  in  Europe  till  years 
afterward.  The  eruption  of  Coseguina  in  the  Bay  of 
Fonseca,  which  began  on  the  19th  of  January,  1835,  and 
lasted  many  days,  was  even  more  dreadful  and  extensive 
in  its  effects  than  that  of  Sumbawa.  The  ashes  during 
this  eruption  were  carried  by  the  upper  current  of  the 
atmosphere  as  far  north  as  Chiassa,  which  is  upward 
of  400  leagues  to  the  windward  of  that  volcano.  Many 
volcanos  supposed  to  be  extinct  have  all  at  once  burst 
out  with  inconceivable  violence.  Witness  Vesuvius,  on 
historical  record ;  and  the  volcano  in  the  island  of  St. 
Vincent  in  our  own  days,  whose  crater  was  lined  with 
large  trees,  and  which  had  not  been  active  in  the  mem- 


248  EARTHQUAKES.  SECT.  XXVI. 

ory  of  man.  Vast  tracts  are  of  volcanic  origin  where 
volcanos  have  ceased  to  exist  for  ages.  Whence  it  may 
be  inferred  that  in  some  places  the  subterraneous  fires 
are  in  the  highest  state  of  activity,  in  some  they  are 
inert,  and  in  others  they  appear  to  be  extinct.  Yet  there 
are  few  countries  that  are  not  subject  to  earthquakes  of 
greater  or  less  intensity ;  the  tremors  are  propagated 
like  a  sonorous  undulation  to  such  distances  that  it  is 
impossible  to  say  in  what  point  they  originate.  In  some 
recent  instances  their  power  must  have  been  tremendous. 
In  South  America,  so  lately  as  1822,  an  area  of  100,000 
square  miles,  which  is  equal  in  extent  to  the  half  of 
France,  was  raised  several  feet  above  its  present  level ; 
a  most  able  account  of  which  is  given  in  the  '  Transac- 
tions of  the  Geological  Society,'  by  an  esteemed  friend 
of  the  author,  Mrs.  Graham,  now  Mrs.  Calcott,  who 
was  present  during  the  whole  time  of  that  formidable 
earthquake,  which  recurred  at  short  intervals  for  more 
than  two  months,  and  who  possesses  talents  to  appre- 
ciate, and  had  opportunities  of  observing,  its  effects 
under  the  most  favorable  circumstances  at  Valparaiso, 
and  for  miles  along  the  coast  where  it  was  most  intense. 
A  considerable  elevation  of  the  land  has  again  taken 
place  along  the  coast  of  Chili,  in  consequence  of  the 
violent  earthquake  which  happened  on  the  20th  of  Feb- 
ruary, 1835.  In  1819,  a  ridge  of  land  stretching  for  50 
miles  across  the  delta  of  the  Indus,  16  feet  broad,  was 
raised  10  feet  above  the  plain;  yet  the  account  of  this 
marvelous  event  was  recently  brought  to  Europe  by 
Mr.  Burnes.  The  reader  is  referred  to  Mr.  L  yell's 
very  excellent  work  on  geology,  already  mentioned,  for 
most  interesting  details  of  the  phenomena  and  extensive 
effects  of  volcanos  and  earthquakes,  too  numerous  to 
find  a  place  here.  It  may  however  be  mentioned,  that 
innumerable  earthquakes  are  from  time  to  time  shaking 
the  solid  crust  of  the  globe,  and  carrying  destruction  to 
distant  regions,  progressively  though  slowly  accomplish- 
ing the  great  work  of  change.  These  terrible  engines 
of  ruin,  fitful  and  uncertain  as  they  may  seem,  must, 
like  all  durable  phenomena,  have  a  law,  which  may  in 
time  be  discovered  by  long-continued  and  accurate  ob- 
servations. 


SKCT.  XXVI.  VOLCANIC  THEORIES.  249 

The  shell  of  volcanic  fire  that  girds  the  globe  at  a 
small  depth  below  our  feet  has  been  attributed  to  differ- 
ent causes.  By  some  it  is  supposed  to  originate  in  an 
ocean  of  incandescent  matter,  still  existing  in  the  cen- 
tral abyss  of  the  earth.  Some  conceive  it  to  be  super- 
ficial, and  due  to  chemical  action,  in  strata  at  no  very 
great  depth  when  compared  with  the  size  of  the  globe. 
The  more  so,  as  matter  on  a  most  extensive  scale  is 
passing  from  old  into  new  combinations,  which,  if  rapidly 
effected,  are  capable  of  producing  the  most  intense  heat. 
According  to  others,  electricity,  which  is  so  universally 
diffused  in  all  its  forms  throughout  the  earth,  if  not  the 
immediate  cause  of  the  volcanic  phenomena,  at  least 
determines  the  chemical  affinities  that  produce  them. 
It  is  clear  that  a  subject  so  involved  in  mystery  must 
give  rise  to  much  speculation,  in  which  every  hypothe- 
sis is  attended  with  difficulties  that  observation  alone 
can  remove. 

But  the  views  of  Mr.  Babbage  and  Sir  John  Herschel 
on  the  general  cause  of  volcanic  action,  and  the  changes 
in  the  equilibrium  of  the  internal  heat  of  the  globe,  ac- 
cord more  with  the  laws  of  mechanics  and  radiant  caloric 
than  any  that  have  been  proposed.  The  theory  of  these 
distinguished  philosophers,  formed  independently  of  each 
other,  is  equally  consistent  with  observed  phenomena, 
whether  the  earth  be  a  solid  crust  encompassing  a  nu- 
cleus of  liquid  lava,  or  that  there  is  merely  a  vast  reser- 
voir or  stratum  of  melted  matter  at  a  moderate  depth 
below  the  superficial  crust.  The  author  is  indebted  to 
the  kindness  of  Mr.  Lyell  for  the  perusal  of  a  most 
interesting  letter  from  Sir  John  Herschel,  in  which  he 
states  his  views  on  the  subject. 

Supposing  that  the  globe  is  merely  a  solid  crust,  rest- 
ing upon  fluid  or  semi-fluid  matter,  whether  extending 
to  the  center  or  not,  the  transfer  of  pressure  from  one 
part  of  its  surface  to  another  by  the  degradation  of  ex- 
isting continents,  and  the  formation  of  new  ones,  would 
be  sufficient  to  subvert  the  equilibrium  of  heat  in  the 
interior,  and  occasion  volcanic  eruptions.  For,  since 
the  internal  heat  of  the  earth  is  transmitted  outwards 
by  radiation,  an  accession  of  new  matter  on  any  part  of 
the  surface,  like  an  addition  of  clothing,  by  keeping  it  in, 


250  VOLCANIC  THEORIES.  SECT.  XXVI. 

would  raise  the  temperature  of  the  strata  below,  and  in 
the  course  of  ages  would  even  reduce  those  at  a  great 
depth  to  a  state  of  fusion.  Some  of  the  substances  might 
be  converted  into  gases  ;  and  should  the  accumulation  of 
new  matter  take  place  at  the  bottom  of  the  sea,  as  is 
generally  the  case,  this  lava  would  be  mixed  with  water 
in  a  state  of  ignition  in  consequence  of  the  enormous 
pressure  of  the  ocean,  and  of  the  newly  superimposed 
matter  which  would  prevent  it  from  expanding  into 
steam.  Now  Mr.  Lyell  has  shown  with  his  usual  talent, 
that  the  quantity  of  matter  carried  down  by  rivers  from 
the  surface  of  the  continents  is  comparatively  trifling, 
and  that  the  great  transfer  to  the  bottom  of  the  ocean  is 
produced  at  the  coast  line  by  the  action  of  the  sea ; 
hence,  says  Sir  John  Herschel,  "  the  greatest  accumula- 
tion of  local  pressure  is  in  the  central  area  of  the  deep 
sea,  while  the  greatest  local  relief  takes  place  along  the 
abraded  coast  lines.  Here  then  should  occur  the  chief 
volcanic  vents."  As  the  crust  of  the  earth  is  much 
weaker  on  the  coasts  than  elsewhere,  it  is  more  easily 
ruptured,  and,  as  Mr.  Babbage  observes,  immense  rents 
might  be  produced  there  by  its  contraction  in  cooling 
down  after  being  deprived  of  a  portion  of  its  original 
thickness.  The  pressure  on  the  bottom  of  the  ocean 
would  force  a  column  of  lava  mixed  with  ignited  water 
and  gas  to  rise  through  an  opening  thus  formed,  and, 
says  Sir  John  Herschel,  "  when  the  column  attains  such 
a  height  that  the  ignited  water  can  become  steam,  the 
joint  specific  gravity  of  the  column  is  suddenly  dimin- 
ished, and  up  comes  a  jet  of  mixed  steam  and  lava,  till 
so  much  has  escaped  that  the  matter  deposited  at  the 
bottom  of  the  ocean  takes  a  fresh  bearing,  when  the 
evacuation  ceases  and  the  crack  becomes  sealed  up." 

This  theory  perfectly  accords  with  the  phenomena  of 
nature,  since  there  are  very  few  active  volcanos  at  a  dis- 
tance from  the  sea,  and  the  exceptions  that  do  occur 
are  generally  near  lakes,  or  they  are  connected  with 
volcanos  on  the  maritime  coasts.  Many  break  out  even 
in  the  bottom  of  the  ocean,  probably  owing  to  some  of  the 
supports  of  the  superficial  crust  giving  way,  so  that  the 
eteam  and  lava  are  forced  up  through  the  fissures. 

Finally,  Mr.  Babbage  observes  that  "  in  consequence 


SKCT.  XXVI.  SUPERFICIAL  HEAT.  251 

of  changes  continually  going  on,  by  the  destruction  of 
forests,  the  filling  up  of  seas,  the  wearing  down  of  ele- 
vated lands,  the  heat  radiated  from  the  earth's  surface 
varies  considerably  at  different  periods.  In  consequence 
of  this  variation,  and  also  in  consequence  of  the  covering 
up  of  the  bottom  of  the  sea  by  the  detritus  of  the  land, 
the  surfaces  of  equal  temperature  within  the  earth  are 
continually  changing  their  form,  and  exposing  thick 
beds  near  the  exterior  to  alterations  of  temperature. 
The  expansion  and  contraction  of  these  strata  may  form 
rents  and  veins,  produce  earthquakes,  determine  vol- 
canic eruptions,  elevate  continents,  and  possibly  raise 
mountain  chains." 

The  numerous  vents  for  the  internal  heat  formed  by 
volcanos,  hot  springs,  and  the  emission  of  steam  so 
frequent  in  volcanic  regions,  no  doubt  maintain  the  tran- 
quillity of  the  interior  fluid  mass,  which  seems  to  be 
perfectly  inert  unless  when  put  in  motion  by  unequal 
pressure. 

But  to  whatever  cause  tha  increasing  heat  of  the 
earth  and  the  subterranean  fires  may  ultimately  be 
referred,  it  is  certain  that,  except  in  some  local  in- 
stances, they  have  no  sensible  effect  on  the  temperature 
of  its  surface.  It  may  therefore  be  concluded  that  the 
heat  of  the  earth  above  the  zone  of  uniform  temperature 
is  entirely  owing  to  the  sun. 

The  powe*of  the  solar  rays  depends  much  upon  the 
manner  in  which  they  fall,  as  we  readily  perceive  from 
the  different  climates  on  our  globe.  The  earth  is  about 
three  millions  of  miles  nearer  to  the  sun  in  winter  than 
in  summer,  but  the  rays  strike  the  northern  hemi- 
sphere more  obliquely  hi  winter  than  in  the  other  half 
of  the  year. 

The  observations  of  the  north  polar  navigators,  and 
those  of  Sir  John  Herscbel  at  the  Cape  of  Good  Hope, 
show  that  the  direct  heating  influence  of  the  solar  rays 
is  greatest  at  the  equator,  and  that  it  diminishes  gradu- 
ally as  the  latitude  increases.  At  the  equator  the 
maximum  is  48|°,  while  in  Europe  it  has  never  ex- 
ceeded 29i°. 

M.  Pouillet  has  estimated  with  singular  ingenuity, 
from  a  series  of  observations  made  by  himself,  that  the 


252  ISOGEOTHERMAL  LINES.  SECT.  XXVI. 

whole  quantity  of  heat  which  the  earth  receives  annu- 
ally from  the  sun  is  such  as  would  be  sufficient  to  melt 
a  stratum  of  ice  covering  the  whole  globe  46  feet  deep. 
Part  of  this  heat  is  radiated  back  into  space ;  but  by  far 
the  greater  part  descends  into  the  earth  during  the 
summer,  toward  the  zone  of  uniform  temperature, 
whence  it  returns  to  the  surface  in  the  course  of  the 
winter,  and  tempers  the  cold  of  the  ground  and  the  at- 
mosphere in  its  passage  to  the  ethereal  regions,  where 
it  is  lost,  or  rather  where  it  combines  with  the  radiation 
from  the  other  bodies  of  the  universe  in  maintaining 
the  temperature  of  space.  The  sun's  power  being 
greatest  between  the  tropics,  the  caloric  sinks  deeper 
there  than  elsewhere,  and  the  depth  gradually  dimin- 
ishes toward  the  poles ;  but  the  heat  is  also  transmitted 
laterally  from  the  warmer  to  the  colder  strata  north  and 
south  of  the  equator,  and  aids  in  tempering  the  severity 
of  the  polar  regions. 

The  mean  heat  of  the  earth  above  the  stratum  of 
constant  temperature  is  determined  from  that  of  springs ; 
and  if  the  spring  be  on  elevated  ground,  the  temperature 
is  reduced  by  computation  to  what  it  would  be  at  the 
level  of  the  sea,  assuming  that  the  heat  of  the  soil 
varies  according  to  the'  same  law  as  the  heat  of  the 
atmosphere,  which  is  about  1°  of  Fahrenheit's  ther- 
mometer for  every  333-7  feet.  From  a  comparison  of 
the  temperature  of  numerous  springs  witk  that  of  the 
air,  Sir  David  Brewster  concludes  that  there  is  a  par- 
ticular line  passing  nearly  through  Berlin,  at  which  the 
temperature  of  springs  and  that  of  the  atmosphere 
coincide  ;  that  in  approaching  the  arctic  circle  the  tem- 
perature of  springs  is  always  higher  than  that  of  the  air, 
while  proceeding  toward  the  equator  it  is  lower. 

Since  the  warmth  of  the  superficial  strata  of  the  earth 
decreases  from  the  equator  to  the  poles,  there  are  many 
places  in  both  hemispheres  where  the  ground  has  the 
same  mean  temperature.  If  lines  were  drawn  through 
all  those  points  in  the  upper  strata  of  the  globe  which 
have  the  same  mean  annual  temperature,  they  would 
be  nearly  parallel  to  the  equator  between  the  tropics, 
and  would  become  more  and  more  irregular  and  sinuous 
toward  the  poles.  These  are  called  isogeothermal  lines. 


S«CT.  XXVI.  CLIMATE.  253 

A  variety  of  local  circumstances  disturb  their  parallelism 
even  between  the  tropics. 

The  temperature  of  the  ground  at  the  equator  is 
Jower  on  the  coasts  and  islands  than  hi  the  interior  of 
continents ;  the  warmest  part  is  in  the  ulterior  of  Africa, 
but  it  is  obviously  affected  by  the  nature  of  the  soil,  es- 
pecially if  it  be  volcanic. 

Much  has  been  done  within  a  few  years  to  ascertain 
the  manner  in  which  heat  is  distributed  over  the  sur- 
face of  our  planet,  and  the  variations  of  climate,  which 
in  a  general  view  mean  every  change  of  the  atmos- 
phere, such  as  of  temperature,  humidity,  variations  ot 
barometric  pressure,  purity  of  ah*,  the  serenity  of  the 
heavens,  the  effects  of  winds,  and  electric  tension. 
Temperature  depends  upon  the  property  which  all 
bodies  possess  more  or  less,  of  perpetually  absorbing  and 
emitting  or  radiating  heat.  When  the  interchange  is 
equal,  the  temperature  of  a  body  remains  the  same ; 
but  when  the  radiation  exceeds  the  absorption,  it  be- 
comes colder,  and  vice  versa.  In  order  to  determine 
the  distribution  of  heat  over  the  surface  of  the  earth,  it 
is  necessary  to  find  a  standard  by  which  the  tempera- 
ture in  different  latitudes  may  be  compared.  For  that 
purpose  it  is  requisite  to  ascertain  by  experiment  the 
mean  temperature  of  the  day,  of  the  month,  and  of  the 
year,  at  as  many  places  as  possible  throughout  the 
earth.  The  annual  average  temperature  may  be  found 
by  adding  the  mean  temperatures  of  all  the  months  hi 
the  year,  and  dividing  the  sum  by  twelve.  The  average 
of  ten  or  fifteen  years  will  give  it  with  tolerable  accu- 
racy ;  for  although  the  temperature  in  any  place  may 
be  subject  to  very  great  variations,  yet  it  never  deviates 
more  than  a  few  degrees  from  its  mean  state,  which 
consequently  offers  a  good  standard  of  comparison. 

If  climate  depended  solely  upon  the  heat  of  the  sun, 
all  places  having  the  same  latitude  would  have  the  same 
mean  annual  temperature.  The  motion  of  the  sun  in 
the  ecliptic  indeed  occasions  perpetual  variations  in  the 
length  of  the  day,  and  in  the  direction  of  the  rays  with 
regard  to  the  earth;  yet,  as  the  cause  is  periodic,  the 
mean  annual  temperature  from  the  sun's  motion  alone 
must  be  constant  in  each  parallel  of  latitude.  For  it  is 
Y 


254  HEAT  DECREASES  WITH  HEIGHT.    SECT.  XXVI. 

evident  that  the  accumulation  of  heat  in  the  long  days  of 
summer,  which  is  but  little  diminished  by  radiation 
during  the  short  nights,  is  balanced  by  the  small  quan- 
tity of  heat  received  during  the  short  days  in  winter, 
and  its  radiation  in  the  long  frosty  and  clear  nights. 
In  fact,  if  the  globe  were  everywhere  on  a  level  with 
the  surface  of  the  sea,  and  of  uniform  substance,  so  as 
to  absorb  and  radiate  heat  equally,  the  mean  heat  of  the 
sun  would  be  regularly  distributed  over  its  surface  in 
zones  of  equal  annual  temperature  parallel  to  the  equa- 
tor, from  which  it  would  decrease  to  each  pole  as  the 
square  of  the  cosine  of  the  latitude ;  and  its  quantity 
would  only  depend  upon  the  altitude  of  the  sun  and 
atmospheric  currents.  The  distribution  of  heat,  how- 
ever, in  the  same  parallel,  is  very  irregular  in  all  lati- 
tudes except  between  the  tropics,  where  the  isothermal 
lines,  or  the  lines  passing  through  places  of  equal  mean 
annual  temperature,  are  more  nearly  parallel  to  the 
equator.  The  causes  of  disturbance  are  very  numerous : 
but  such  as  have  the  greatest  influence,  according  to  M. 
de  Humboldt,  to  whom  we  are  indebted  for  the  greater 
part  of  what  is  known  on  the  subject,  are  the  elevation 
of  the  continents,  the  distribution  of  land  and  water 
over  the  surface  of  the  globe  exposing  different  absorb- 
ing and  radiating  powers ;  the  variations  in  the  surface 
of  the  land,  as  forests,  sandy  deserts,  verdant'  plains, 
rocks,  &c.  ;  mountain-chains  covered  with  masses  of 
snow,  which  diminish  the  temperature ;  the  reverbera- 
tion of  the  sun's  rays  in  the  valleys,  which  increases  it; 
and  the  interchange  of  currents,  both  of  air  and  water, 
which  mitigates  the  rigor  of  climates ;  the  warm  cur- 
rents from  the  equator  softening  the  severity  of  the 
polar  frosts,  and  the  cold  currents  from  the  poles  tem- 
pering the  intense  heat  of  the  equatorial  regions.  To 
these  may  be  added  cultivation,  though  its  influence 
extends  over  but  a  small  portion  of  the  globe,  only  a 
fourth  part  of  the  land  being  inhabited. 

Temperature  decreases  with  the  height  above  the 
level  of  the  sea,  as  well  as  with  the  latitude.  The  air 
in  the  higher  regions  of  the  atmosphere  is  much  cooler 
than  that  below,  because  the  warm  air  expands  as  it 
rises,  by  which  its  capacity  for  heat  is  increased,  a  great 


S»CT.  XXVI.         LINE  OF  PERPETUAL  SNOW.  255 

proportion  becomes  latent,  and  less  of  it  sensible.  A 
portion  of  air  at  the  surface  of  the  earth  whose  temper- 
ature is  70°  of  Fahrenheit,  if  carried  to  the  height  of 
two  miles  and  a  half,  would  expand  so  much  that  its  tem- 
perature would  be  reduced  50°  ;  and  in  the  ethereal 
regions  the  temperature  is  90°  below  the  point  of  con- 
gelation. 

The  height  at  which  snow  lies  perpetually  decreases 
from  the  equator  to  the  poles,  and  is  higher  in  summer 
than  in  winter ;  but  it  varies  from  many  circumstances. 
Snow  rarely  falls  when  the  cold  is  intense  and  the  at- 
mosphere dry.  Extensive  forests  produce  moisture  by 
their  evaporation ;  and  high  table-lands,  on  the  contrary, 
dry  and  warm  the  ah*.  In  the  Cordilleras  of  the  Andes, 
plains  of  only  twenty-five  square  leagues  raise  the  tem- 
perature as  much  as  3°  or  4°  above  what  is  found  at  the 
same  altitude  on  the  rapid  declivity  of  a  mountain,  con- 
sequently the  line  of  perpetual  snow  varies  according  as 
one  or  other  of  these  causes  prevails.  Aspect  in  gen- 
eral has  also  a  great  influence  ;  yet,  according  to  M. 
Jacquemont,  the  line  of  perpetual  snow  is  much  higher 
on  the  northern  than  on  the  southern  side  of  the  Hima- 
laya mountains.  On  the  whole,  it  appears  that  the  mean 
height  between  the  tropics  at  which  the  snow  lies  per- 
petually is  about  15,207  feet  above  the  level  of  the  sea ; 
whereas  snow  does  not  cover  the  ground  continually  at 
the  level  of  the  ocean  till  near  the  north  pole.  In  the 
southern  hemisphere,  however,  the  cold  is  greater  than 
in  the  northern.  In  Sandwich  Land,  between  the  54th 
and  58th  degrees  of  latitude,  perpetual  snow  and  ice  ex- 
tend to  the  sea-beach ;  and  in  the  island  of  St.  George's, 
in  the  53rd  degree  of  south  latitude,  which  corresponds 
with  the  latitude  of  the  central  counties  of  England,  per- 
petual snow  descends  even  to  the  level  of  the  ocean.  It 
has  been  shown  that  this  excess  of  cold  in  the  southern 
hemisphere  cannot  be  attributed  to  the  winter  being 
longer  than  ours  by  7|  days.  It  is  probably  owing  to 
the  ice  being  more  extensive  at  the  south  than  the  north 
pole,  and  to  the  open  sea  surrounding  it,  which  permits 
the  icebergs  to  descend  to  a  lower  latitude  by  10°  than 
they  do  in  the  northern  hemisphere,  on  account  of  the 
numerous  obstructions  opposed  to  them  by  the  islands 


256  EFFECTS  OF  THE  OCEAN.  SKCT.  XXVI. 

and  continents  about  the  north  pole.  Icebergs  seldom 
float  farther  to  the  south  than  the  Azores  ;  whereas 
those  that  come  from  the  south  pole  descend  as  far  as 
the  Cape  of  Good  Hope,  and  occasion  a  continual  ab- 
sorption of  heat  in  melting. 

The  influence  of  mountain-chains  does  not  wholly 
depend  upon  the  line  of  perpetual  congelation.  They 
attract  and  condense  the  vapors  floating  in  the  air,  and 
send  them  down  in  torrents  of  rain.  They  radiate  heat 
into  the  atmosphere  at  a  lower  elevation,  and  increase 
the  temperature  of  the  valleys  by  the  reflection  of  the 
sun's  rays,  and  by  the  shelter  they  afford  against  pre- 
vailing winds.  But  on  the  contrary,  one  of  the  most 
general  and  powerful  causes  of  cold  arising  from  the  vi- 
cinity of  mountains,  is  the  freezing  currents  of  wind 
which  rush  from  their  lofty  peaks  along  the  rapid  decliv- 
ities, chilling  the  surrounding  valleys  :  such  is  the  cut- 
ting north  wind  called  the  bise  in  Switzerland. 

Next  to  elevation,  the  difference  in  the  radiating  and 
absorbing  powers  of  the  sea  and  land  has  the  greatest 
influence  in  disturbing  the  regular  distribution  of  heat. 
The  extent  of  the  dry  land  is  not  above  the  fourth  part 
of  that  of  the  ocean  ;  so  that  the  general  temperature 
of  the  atmosphere,  regarded  as  the  result  of  the  partial 
temperatures  of  the  whole  surface  of  the  globe,  is  most 
powerfully  modified  by  the  sea.  Besides,  the  ocean 
acts  more  uniformly  on  the  atmosphere  than  the  diver- 
sified surface  of  the  solid  mass  does,  both  by  the  equality 
of  its  curvature  and  its  homogeneity.  In  opaque  sub- 
stances the  accumulation  of  heat  is  confined  to  the 
stratum  nearest  the  surface.  The  seas  become  less 
heated  At  their  surface  than  the  land,  because  the  solar 
rays,  before  being  extinguished,  penetrate  the  trans- 
parent liquid  to  a  greater  depth  and  in  greater  numbers 
than  in  the  opaque  masses.  On  the  other  hand,  water 
has  a  considerable  radiating  power,  which,  together 
with  evaporation,  would  reduce  the  surface  of  the  ocean 
to  a  very  low  temperature,  if  the  cold  particles  did  not 
sink  to  the  bottom  on  account  of  their  superior  density. 
The  seas  preserve  a  considerable  portion  of  the  heat 
they  receive  in  summer,  and  from  their  saltness  do  not 
freeze  so  soon  as  fresh  water.  So  that  in  consequence 


SKCT.  XXVI.       TEMPERATURE  OF  THE  LAND.  257 

of  all  these  circumstances,  the  ocean  is  not  subject  to 
such  variations  of  heat  as  the  land ;  and  by  imparting 
its  temperature  to  the  winds,  it  diminishes  the  rigor  of 
climate  on  the  coasts  and  in  the  islands,  which  are 
never  subject  to  such  extremes  of  heat  and  cold  as  are 
experienced  in  the  interior  of  continents,  though  they 
are  liable  to  fogs  and  rain  from  the  evaporation  of  the 
adjacent  seas.  On  each  side  of  the  equator  to  the  48th 
degree  of  latitude,  the  surface  of  the  ocean  is  in  gene- 
ral warmer  than  the  air  above  it.  The  mean  of  the 
difference  of  the  temperature  at  noon  and  midnight  is 
about  l°-37,  the  greatest  deviation  never  exceeding  from 
0°-36  to  2°'16,  which  is  much  cooler  than  the  air  over 
the  land. 

On  land  the.  temperature  depends  upon  the  nature 
of  the  soil  and  its  products,  its  habitual  moisture  or  dry- 
ness.  From  the  eastern  extremity  of  the  Sahara 
desert  quite  across  Africa,  the  soil  is  almost  entirely 
barren  sand ;  and  the  Sahara  desert  itself,  without  in- 
cluding Dafour  or  Dongola,  extends  over  an  area  of 
194,000  square  leagues,  equal  to  twice  the  area  of  the 
Mediterranean  Sea,  and  raises  the  temperature  of  the 
air  by  radiation  from  90°  to  100°,  which  must  have  a 
most  extensive  influence.  On  the  contrary,  vegetation 
cools  the  air  by  evaporation  and  the  apparent  radiation 
of  cold  from  the  leaves  of  plants,  because  they  absorb 
more  caloric  than  they  give  out.  The  graminiferous 
plains  of  South  America  cover  an  extent  ten  times 
greater  than  France,  occupying  no  less  than  about 
50,000  square  leagues,  which  is  more  than  the  whole 
chain  of  the  Andes,  and  all  the  scattered  mountain- 
groups  of  Brazil.  The'se,  together  with  the  plains  of 
North  America  and  the  steppes  of  Europe  and  Asia, 
must  have  an  extensive  cooling  effect  on  the  atmosphere 
if  it  be  considered  that  in  calm  and  serene  nights  they 
cause  the  thermometer  to  descend  12°  or  14°,  and  that 
in  the  meadows  and  heaths  in  England  the  absorption 
of  heat  by  the  grass  is  sufficient  to  cause  the  tempera- 
ture to  sink  to  the  point  of  congelation  during  the  night 
for  ten  months  in  the  year.  Forests  cool  the  air  also 
by  shading  the  ground  from  the  rays  of  the  sun,  and  by 
evaporation  from  the  boughs.  Hales  found  that  the 
17  Y  2 


258        CONFIGURATION  OF  LAND  AND  WATER.    SECT.  XXVI. 

leaves  of  a  single  plant  of  helianthus  three  feet  high  ex- 
posed nearly  forty  feet  of  surface ;  and  if  it  be  con- 
sidered that  the  woody  regions  of  the  river  Amazons, 
and  the  higher  part  of  the  Oroonoko,  occupy  an  area  of 
260,000  square  leagues,  some  idea  may  be  formed  of 
the  torrents  of  vapor  which  rise  from  the  leaves  of  the 
forests  all  over  the  globe.  However,  the  frigorific 
effects  of  their  evaporation  are  counteracted  in  some 
measure  by  the  perfect  calm  which  reigns  in  the  tropi- 
cal wildernesses.  The  innumerable  rivers,  lakes,  pools, 
and  marshes  interspersed  through  the  continents  absorb 
caloric,  and  cool  the  air  by  evaporation  ;  but  on  account 
of  the  chilled  and  dense  particles  sinking  to  the  bottom, 
deep  water  diminishes  the  cold  of  winter,  so  long  as  ice 
is  not  formed. 

In  consequence  of  the  difference  in  the  radiatmg  and 
absorbing  powers  of  the  sea  and  land,  their  configuration 
greatly  modifies  the  distribution  of  heat  over  the  surface 
of  the  globe.  Under  the  equator  only  one- sixth  part  of 
the  circumference  is  land  ;  and  the  superficial  extent  of 
land  in  the  northern  and  southern  hemispheres  is  in  the 
proportion  of  three  to  one.  The  effect  of  this  unequal 
division  is  greater  in  the  temperate  than  in  the  torrid 
zones,  for  the  area  of  land  iu  the  northern  temperate 
zone  is  to  that  in  the  southern  as  thirteen  to  one,  where- 
as the  proportion  of  land  between  the  equator  and  each 
tropic  is  as  five  to  four.  It  is  a  curious  fact  noticed  by 
Mr.  Gardner,  that  only  one  twenty-seventh  part  of  the 
land  of  the  globe  has  land  diametrically  opposite  to  it. 
This  disproportionate  arrangement  of  the  solid  part  of 
the  globe  has  a  powerful  influence  on  the  temperature 
of  the  southern  hemisphere.  But  besides  these  greater 
modifications,  the  peninsulas,  promontories,  and  capes, 
running  out  into  the  ocean,  together  with  bays  and  in- 
ternal seas,  all  affect  temperature.  To  these  may  be 
added  the  position  of  continental  masses  with  regard  to 
the  cardinal  points.  All  these  diversities  of  land  and 
water  influence  temperature  by  the  agency  of  the  winds. 
On  this  account  the  temperature  is  lower  on  the  eastern 
coasts  both  of  the  New  and  Old  World  than  on  the 
western  ;  for  considering  Europe  as  an  island,  the  gen- 
eral temperature  is  mild  in  proportion  as  the  aspect  is 


SECT.  XXVI.  ISOTHERMAL  LINES.  259 

open  to  the  western  ocean,  the  superficial  temperature 
of  which,  as  far  north  as  the  45th  and  50th  degrees  of 
latitude,  does  not  fall  below  48°  or  51°  of  Fahrenheit, 
even  in  the  middle  of  winter.  On  the  contrary,  the 
cold  of  Russia  arises  from  its  exposure  to  the  northern 
and  eastern  winds.  But  the  European  part  of  that  em- 
pire has  a  less  rigorous  climate  than  the  Asiatic,  because 
it  does  not  extend  to  so  high  a  latitude. 

The  interposition  of  the  atmosphere  modifies  all  the 
effects  of  the  sun's  heat.  The  earth  communicates  its 
temperature  so  slowly  that  M.  Arago  has  occasionally 
found  as  much  as  from  14°  to  18°  of  difference  between 
the  heat  of  the  soil  and  that  of  the  air  two  or  three 
inches  above  it. 

The  circumstances  which  have  been  enumerated,  and 
many  more,  concur  in  disturbing  the  regular  distribution 
of  heat  over  the  globe,  and  occasion  numberless  local  ir- 
regularities. Nevertheless  the  mean  annual  temperature 
becomes  gradually  lower  from  the  equator  to  the  poles. 
But  the  diminution  of  mean  heat  is  most  rapid  between 
the  40th  and  45th  degrees  of  latitude  both  in  Europe 
and  America,  which  accords  perfectly  with  theory; 
whence  it  appears  that  the  variation  in  the  square  of 
the  cosine  of  the  latitude  (N.  123),  which  expresses  the 
law  of  the  change  of  temperature,  is  a  maximum  to- 
ward the  45th  degree  of  latitude.  The  mean  annual 
temperature  under  the  line  in  America  is  about  81^°  of 
Fahrenheit :  in  Africa  it  is  said  to  be  nearly  83°.  "The 
difference  probably  arises  from  the  winds  of  Siberia  and 
Canada,  whose  chilly  influence  is  sensibly  felt  in  Asia 
and  America,  even  within  18°  of  the  equator. 

The  isothermal  lines  are  nearly  parallel  to  the  equator, 
till  about  the  22d  degree  of  latitude  on  each  side  of  it, 
where  they  begin  to  lose  their  parallelism,  and  continue 
to  do  so  more  and  more  as  the  latitude  augments. 
With  regard  to  the  northern  hemisphere,  the  isother- 
mal line  of  59°  of  Fahrenheit  passes  between  Rome  and 
Florence  in  latitude  43° ;  and  near  Raleigh  in  North 
Carolina,  latitude  36°  :  that  of  50°  of  equal  annual  tem- 
perature runs  through  the  Netherlands,  latitude  51°; 
and  near  Boston  in  the  United  States,  latitude  42£°  : 
that  of  41°  passes  near  Stockholm,  latitude  59|°  ;  and 


260  ISOTHERMAL  LINES.  SECT.  XXVI. 

St.  George's  Bay,  Newfoundland,  latitude  48° :  and 
lastly,  the  line  of  32°,  the  freezing  point  of  water,  passes 
between  Ulea  in  Lapland,  latitude  66°,  and  Table  Bay, 
on  the  coast  of  Labrador,  latitude  54°. 

Thus  it  appears  that  the  isothermal  lines,  which  are 
nearly  parallel  to  the  equator  for  about  22°,  afterward 
deviate  more  and  more.  From  the  observations  of  Sir 
Charles  Giesecke  in  Greenland,  of  Captain  Scoresby  in 
the  Arctic  Seas,  and  also  from  those  of  Sir  Edward 
Parry  and  Sir  John  Franklin,  it  is  found  that  the  iso- 
thermal lines  of  Europe  and  America  entirely  separate 
in  the  high  latitudes,  and  surround  two  poles  of  max- 
imum cold,  one  in  America  and  the  other  in  the  north 
of  Asia,  neither  of  which  coincides  with  the  pole  of  the 
earth's  rotation.  These  poles  are  both  situate  in  about 
the  80th  parallel  of  north  latitude.  The  transatlantic 
pole  is  in  the  100th  degree  of  west  longitude,  about 
5°  to  the  north  of  Sir  Graham  Moore's  Bay,  in  the 
Polar  Seas ;  and  the  Asiatic  pole  is  in  the  95th  degree 
of  east  longitude,  a  little  to  the  north  of  the  Bay  of  Tai- 
mura,  near  the  North-east  Cape.  According  to  the 
estimation  of  Sir  David  Brewster,  from  the  observations 
of  M.  de  Humboldt  and  Captains  Parry  and  Scoresby, 
the  mean  annual  temperature  of  the  Asiatic  pole  is 
nearly  1°  of  Fahrenheit's  thermometer,  and  that  of  the 
transatlantic  pole  about  3^°  below  zero,  whereas  he  sup- 
poses the  mean  annual  temperature  of  the  pole  of  rota- 
tion to  be  4°  or  5°.  It  is  believed  that  two  correspond- 
ing poles  of  maximum  cold  exist  in  the  southern  hemis- 
phere, though  observations  are  wanting  to  trace  the 
course  of  the  southern  isothermal  lines  with  the  same 
accuracy  as  the  northern. 

The  isothermal  lines,  or  such  as  pass  through  places 
where  the  mean  annual  temperature  of  the  air  is  the 
same,  do  not  always  coincide  with  the  isogeothermal 
lines,  which  are  those  passing  through  places  where  the 
mean  temperature  of  the  ground  is  the  same.  Sir 
David  Brewster,  in  discussing  this  subject,  finds  that 
the  isogeothermal  lines  are  always  parallel  to  the  iso- 
thermal lines ;  consequently  the  same  general  formula 
will  serve  to  determine  both,  since  the  difference  is  a 
constant  quantity  obtained  by  observation,  and  depend- 


SECT.  XXVI.  EXCESSIVE  CLIMATES.  261 

ing  upon  the  distance  of  the  place  from  the  neutral  iso- 
thermal line.  These  results  are  confirmed  by  the  ob- 
servations of  M.  Kupffer  of  Kasan  during  his  excursions 
to  the  north,  which  show  that  the  European  and  the 
American  portions  of  the  isogeothermal  line  of  32°  of 
Fahrenheit  actually  separate,  and  go  round  the  two 
poles  of  maximum  cold.  This  traveler  remarked,  also, 
that  the  temperature  both  of  the  air  and  of  the  soil  de- 
creases most  rapidly  toward  the  45th  degree  of  latitude. 

It  is  evident  that  places  may  have  the  same  mean  an- 
nual temperature,  and  yet  differ  materially  in  climate. 
In  one,  the  winters  may  be  mild,  and  the  summers  cool ; 
whereas  another  may  experience  the  extremes  of  heat 
and  cold.  Lines  passing  through  places  having  the 
same  mean  summer  or  winter  temperature,  are  neither 
parallel  to  the  isothermal,  the  geothermal  lines,  nor  to  one 
another,  and  they  differ  still  more  from  the  parallels  of 
latitude.  In  Europe,  the  latitude  of  two  places  which 
have  the  same  annual  heat  never  differs  more  than  8°  or 
9° ;  whereas  the  difference  in  the  latitude  of  those  having 
the  same  mean  winter  temperature  is  sometimes  as 
much  as  18°  or  19°.  At  Kasan  in  the  interior  of  Rus- 
sia, in  latitude  55°-48,  nearly  the  same  with  that  of 
Edinburgh,  the  mean  annual  temperature  is  about  37°-6 ; 
at  Edinburgh  it  is  47°-84.  At  Kasan,  the  mean  sum- 
mer temperature  is  64°-84,  and  that  of  winter  2°-12; 
whereas  at  Edinburgh  the  mean  summer  temperature 
is  58°-28,  and  that  of  winter  38°-66.  Whence  it  ap- 
pears that  the  difference  of  winter  temperature  is  much 
greater  than  that  of  summer.  At  Quebec,  the  sum- 
mers are  as  warm  as  those  in  Paris,  and  grapes  some- 
times ripen  in  the  open  air :  whereas  the  winters  are 
as  severe  as  in  Petersburgh ;  the  snow  lies  five  feet 
deep  for  several  months,  wheel  carriages  cannot  be  used, 
the  ice  is  too  hard  for  skating,  traveling  is  performed  in 
sledges,  and  frequently  on  the  ice  of  the  river  St.  Law- 
rence. The  cold  at  Melville  Island  on  the  15th  of  Jan- 
uary, 1820,  according  to  Sir  Edward  Parry,  was  55° 
below  the  zero  of  Fahrenheit's  thermometer,  only  3° 
above  the  temperature  of  the  ethereal  regions,  yet  the 
summer  heat  in  these  high  latitudes  is  insupportable. 

Observations  tend  to  prove  that  all  the  climates  of  the 


2G.2      INFLUENCE  OF  HEAT  ON  VEGETATION.  SKCT.  XXVII. 

earth  are  stable,  and  that  their  vicissitudes  are  only 
periods  or  oscillations  of  more  or  less  extent,  which  van- 
ish in  the  mean  annual  temperature  of  a  sufficient  num- 
ber of  years.  This  constancy  of  the  mean  annual  temper- 
ature of  the  different  places  on  the  surface  of  the  globe 
shows  that  the  same  quantity  of  heat,  which  is  annually 
received  by  the  earth,  is  annually  radiated  into  space. 
Nevertheless  a  variety  of  causes  may  disturb  the  climate 
of  a  place;  cultivation  may  make  it  warmer;  but  it  is 
at  the  expense  of  some  other  place,  which  becomes 
colder  in  the  same  proportion.  There  may  be  a  suc- 
cession of  cold  summers  and  mild  winters,  but  in  some 
other  country  the  contrary  takes  place  to  effect  the 
compensation  ;  wind,  rain,  snow,  fog,  and  the  other  me- 
teoric phenomena,  are  the  ministers  employed  to  accom- 
plish the  changes.  The  distribution  of  heat  may  vary 
with  a  variety  of  circumstances  ;  but  the  absolute  quan- 
tity lost  and  gained  by  the  whole  earth  in  the  course  of 
a  year  is  invariably  the  same. 


SECTION  XXVII. 

Influence  of  Temperature  on  Vegetation — Vegetation  varies  with  the  Lati 
tude  and  Height  above  the  Sea — Geographical  Distribution  of  Land 
Plants — Distribution  of  Marine  Plants— Corallines,  Shell-fish,  Reptiles, 
Insects,  Birds,  and  Quadrupeds — Varieties  of  Mankind,  yet  Identity  of 
Species. 

THE  gradual  decrease  of  temperature  in  the  air  and  in 
the  earth,  from  the  equator  to  the  poles,  is  clearly  indi- 
cated by  its  influence  on  vegetation.  In  the  valleys  of 
the  torrid  zone,  where  the  mean  annual  temperature  is 
very  high,  and  where  there  is  abundance  of  light  and 
moisture,  nature  adorns  the  soil  with  all  the  luxuriance 
of  perpetual  summer.  The  palm,  the  bombax  ceiba, 
and  a  variety  of  magnificent  trees,  tower  to  the  height 
of  150  or  200  feet  above  the  banana,  the  bamboo,  the 
arborescent  fern,  and  numberless  other  tropical  produc- 
tions, so  interlaced  by  creeping  and  parasitical  plants  as 
often  to  present  an  impenetrable  barrier.  But  the 
richness  of  vegetation  gradually  diminishes  with  the  tem- 
perature •  the  splendor  of  the  tropical  forest  is  succeeded 


SECT.  XXVII.    LIGHT  REQUISITE  FOR  PLANTS.  263 

by  the  regions  of  the  olive  and  vine ;  these  again  yield 
to  the  verdant  meadows  of  more  temperate  climes ;  then 
follow  the  birch  and  the  pine,  which  probably  owe  their 
existence  in  very  high  latitudes  more  to  the  warmth  of 
the  soil  than  to  that  of  the  air.    But  even  these  enduring 
plants  become  dwarfish  stunted  shrubs,  till  a  verdant 
carpet  of  mosses  and  lichens,  enameled  with  flowers, 
exhibits  the  last  sign  of  vegetable  life  during  the  short 
but  fervent  summers  at  the  polar  regions.     Such  is  the 
effect  of  cold  and  diminished  light  on  the  vegetable  king- 
dom, that  the  number  of  species   growing  under  the 
line,  and  in  the  northern  latitudes  of  45°  and  68°,  are  in 
the  proportion  of  the  numbers  12,  4,  and  1.     Notwith- 
standing the  remarkable  difference  between  a  tropical 
and  polar  Flora,  light  and  moisture  seem  to  be  almost  the 
only  requisites  for  vegetation,  since  neither  heat,  cold, 
nor  even  comparative  darkness,  absolutely  destroy  the 
fertility  of  nature.      In  salt  plains  and  sandy  deserts 
alone,  hopeless  barrenness  prevails.    JPlants  grow  on  the 
borders  of  hot  springs — they  form  the  oasis  wherever 
moisture  exists,  among  the  burning  sands  of  Africa — 
they  are  found  in  caverns  almost  void  of  light,  though 
generally  blanched  and  feeble.     The  ocean  teems  with 
vegetation.     The  snow  itself  not  only  produces  a  red 
alga,  discovered  by  Saussure  in  the  frozen  declivities  of 
the  Alps,  found  in  abundance  by  the  author  crossing 
the  Col  de  Bonhomme  from  Savoy  to  Piedmont,  and  by 
the  polar  navigators  in  the  Arctic  regions,  but  it  affords 
shelter  to  the  productions  of  those  inhospitable  climes 
against  the  piercing  winds  that  sweep  over  fields  of  ever- 
lasting ice.     Those  interesting  mariners  narrate,  that 
ander  this  cold  defence  plants  spring  up,  dissolve  the 
snow  a  few  inches  round,   and  the  part  above  being 
again  quickly  frozen  into  a  transparent  sheet  of  ice,  ad- 
mits the  sun's  rays,  which  warm  and  cherish  the  plants 
in  this  natural  hot-house,  till  the  returning  summer  ren- 
ders such  protection  unnecessary. 

The  chemical  action  of  light  is,  however,  absolutely 
requisite  for  the  growth  of  plants  which  derive  their 
principal  nourishment  from  the  atmosphere.  They  con- 
sume carbonic  acid  gas,  vapor,  nitrogen,  and  the  ammo- 
nia it  contains  ;  but  it  is  the  chemical  agency  of  light 


264  DISTRIBUTION  OF  PLANTS.         SECT.  XXVII. 

that  enables  them  to  absorb,  decompose,  and  consolidate 
these  substances  into  wood,  leaves,  flowers,  and  fruit. 
The  atmosphere  would  soon  be  deprived  of  these  ele- 
ments of  vegetable  life,  were  they  not  perpetually  sup- 
plied by  the  animal  creation ;  while  in  return,  plants 
decompose  the  moisture  they  imbibe,  and  having  assim- 
ilated the  carbonic  acid  gas,  they  exhale  oxygen  for  the 
maintenance  of  the  animated  creation,  and  thus  preserve 
a  just  equilibrium.  Hence  it  is  the  powerful  and  com- 
bined influences  of  the  whole  solar  beams  that  give  such 
brilliancy  to  the  tropical  forests,  while  with  their  de- 
creasing energy  in  the  higher  latitudes,  vegetation  be- 
comes less  and  less  vigorous. 

By  far  the  greater  part  of  the  hundred  and  ten  thou- 
sand known  species  of  plants  are  indigenous  in  Equinoctial 
America.  Europe  contains  about  half  the  number ;  Asia 
with  its  islands,  somewhat  less  than  Europe;  New 
Holland  with  the  islands  in  the  Pacific,  still  less  ;  and  in 
Africa  there  are  fewer  vegetable  productions  than  in 
any  part  of  the  globe  of  equal  extent.  Very  few  social 
plants,  such  as  grasses  and  heaths,  that  cover  large 
tracts  of  land,  are  to  be  found  between  the  tropics,  ex- 
cept on  the  sea-coasts  and  elevated  plains  :  some  excep- 
tions to  this,  however,  are  to  be  met  with  in  the  jungles 
of  the  Deccan,  Khandish,  &c.  In  the  equatorial  regions, 
where  the  heat  is  always  great,  the  distribution  of  plants 
depends  upon  the  mean  annual  temperature ;  whereas 
in  temperate  zones  the  distribution  is  regulated  in  some 
dogree  by  the  summer  heat.  Some  plants  require  a 
gentle  warmth  of  long  continuance,  others  flourish  most 
where  the  extremes  of  heat  and  cold  are  greater.  The 
range  of  wheat  is  very  great :  it  may  be  cultivated  as  far 
north  as  the  60th  degree  of  latitude,  but  in  the  ton-id 
zone  it  will  seldom  form  an  ear  below  an  elevation  of 
4500  feet  above  the  level  of  the  sea,  from  exuberance  of 
vegetation  ;  nor  will  it  ripen  above  the  height  of  10,800 
feet,  though  much  depends  upon  local  circumstances. 
Colonel  Sykes  states  that  in  the  Deccan  wheat  thrives 
1800  feet  above  the  level  of  the  sea.  The  best  wines 
are  produced  between  the  30th  and  45th  degrees  of 
north  latitude.  With  regard  to  the  vegetable  kingdom, 
elevation  is  equivalent  to  latitude,  as  far  as  temperature 


SICT.  XXVII.          DISTRIBUTION  OF  PLANTS.  265 

is  concerned.  In  ascending  the  mountains  of  the  torrid 
zone,  the  richness  of  the  tropical  vegetation  diminishes 
with  the  height ;  a  succession  of  plants  similar  to,  though 
not  identical  with,  those  found  in  latitudes  of  corre- 
sponding mean  temperature  takes  place  ;  the  lofty  for- 
ests by  degrees  lose  their  splendor,  stunted  shrubs  suc- 
ceed, till  at  last  the  progress  of  the  lichen  is  checked  by 
eternal  snow.  On  the  volcano  of  TenerifFe  there  are 
five  successive  zones,  each  producing  a  distinct  race  of 
plants.  The  first  is  the  region  of  vines,  the  next  that 
of  laurels ;  these  are  followed  by  the  districts  of  pines, 
of  mountain  broom,  and  of  grass  ;  the  whole  covering  the 
declivity  of  the  peak  through  an  extent  of  11,200  feet  of 
perpendicular  height. 

Near  the  equator,  the  oak  flourishes  at  the  height  of 
9200  feet  above  the  level  of  the  sea,  and  on  the  lofty 
range  of  the  Himalaya,  the  primula,  the  convallaria,  and 
the  veronica  blossom,  but  not  the  primrose,  the  lily  of 
the  valley,  or  the  veronica  which  adorn  our  meadows  : 
for  although  the  herbarium  collected  by  Mr.  Moorcroft, 
on  his  route  from  Neetee  to  Daba  and  Garlope  in  Chi- 
nese Tartary,  at  elevations  as  high  or  even  higher  than 
Mont  Blanc,  abounds  in  Alpine  and  European  genera, 
the  species  are  universally  different,  with  the  single 
exception  of  the  rhodiola  rosea,  which  is  identical  with 
the  species  that  blooms  in  Scotland.  It  is  not  in  this 
instance  alone  that  similarity  of  climate  obtains  without 
identity  of  productions  ;  throughout  the  whole  globe,  a 
certain  analogy  both  of  structure  and  appearance  is  fre- 
quently discovered  between  plants  under  corresponding 
circumstances,  which  are  yet  specifically  different.  It 
is  even  said  that  a  distance  of  25°  of  latitude  occasions  a 
total  change,  not  only  of  vegetable  productions,  but  of 
organized  beings.  Certain  it  is,  that  each  separate  re- 
gion both  of  land  and  water,  from  the  frozen  shores  of 
the  polar  circles  to  the  burning  regions  of  the  torrid 
zone,  possesses  a  Flora  of  species  peculiarly  its  own. 
The  whole  globe  has  been  divided  by  botanical  geogra- 
phers into  twenty-seven  botanical  districts  differing  al- 
most entirely  in  their  specific  vegetable  productions  ;  the 
limits  of  which  are  most  decided  when  they  are  sepa- 
rated by  a  wide  expanse  of  ocean,  mountain-chains, 
Z 


266  DISTRIBUTION  OF  PLANTS.          SECT.  XXVII. 

sandy  deserts,  salt  plains,  or  internal  seas.  A  consider- 
able number  of  plants  are  common  to  the  northern  re- 
gions of  Asia,  Europe,  and  America,  where  the  continents 
almost  unite ;  but  in  approaching  the  south,  the  Floras 
of  these  three  great  divisions  of  the  globe  differ  more 
and  more  even  in  the  same  parallels  of  latitude,  which 
shows  that  temperature  alone  is  not  the  cause  of  the  al- 
most complete  diversity  of  species  that  everywhere  pre- 
vails. The  Floras  of  China,  Siberia,  Tartary,  of  the 
European  district  including  Central  Europe,  and  the 
coast  of  the  Mediterranean,  and  the  Oriental  region, 
comprising  the  countries  round  the  Black  and  Caspian 
Seas,  all  differ  in  specific  character.  Only  twenty -four 
species  were  found  by  MM.  Bonpland  and  Humboldtin 
Equinoctial  America  identical  with  those  of  the  old 
world:  and  Mr.  Brown  not  only  found  that  a  peculiar 
vegetation  exists  in  New  Holland,  between  the  33d  and 
35th  parallels  of  south  latitude,  but  that,  at  the  eastern 
and  western  extremities  of  these  parallels,  not  one  spe- 
cies is  common  to  both,  and  that  certain  genera  also  are 
almost  entirely  confined  to  these  spots.  The  number  of 
species  common  to  Australia  and  Europe  are  only  166 
out  of,4100,  and  probably  some  of  these  have  been  con- 
veyed thither  by  the  colonists.  This  proportion  exceeds 
what  is  observed  in  Southern  Africa,  and  from  what  has 
been  already  stated,  the  proportion  of  European  species 
in  Equinoctial  America  is  still  less. 

Islands  partake  of  the  vegetation  of  the  nearest  con- 
tinents, but  when  very  remote  from  land  their  Floras 
are  altogether  peculiar.  The  Aleutian  Islands,  extend- 
ing between  Asia  and  America,  partake  of  the  vegeta- 
tion of  the  northern  parts  of  both  these  continents,  and 
may  have  served  as  a  channel  of  communication.  In 
Madeira  and  Teneriffe,  the  plants  of  Portugal,  Spain, 
the  Azores,  and  of  the  north  coast  of  Africa  are  found  ; 
and  the  Canaries  contain  a  great  number  of  plants  be- 
longing to  the  African  coast.  But  each  of  these  islands 
possesses  a  Flora  that  exists  nowhere  else ;  and  St. 
Helena,  standing  alone  in  the  midst  of  the  Atlantic 
Ocean,  out  of  sixty-one  indigenous  species,  produces 
only  two  or  three  recognized  as  belonging  to  any  other 
part  of  the  world. 


SECT.  XXVII.    DISTRIBUTION  OF  MARINE  PLANTS.  267 

Tt  appears  from  the  investigations  of  M.  de  Humboldt, 
that  between  the  tropics  the  monocotyledonous  plants, 
such  as  grasses  and  palms  which  have  only  one  seed- 
lobe,  are  to  the  dicotyledonous  tribe,  which  have  two 
seed-lobes  like  most  of  the  European  species,  in  the 
proportion  of  one  to  four  ;  in  the  temperate  zones  they 
are  as  one  to  six;  and  in  the  Arctic  regions,  where 
mosses  and  lichens  which  form  the  lowest  order  of  the 
vegetable  creation  abound,  the  proportion  is  as  one  to 
two.  The  annual  monocotyledooous  and  dicotyledonous 
plants  in  the  temperate  zones  amount  to  one-sixth  of 
the  whole,  omitting  the  Cryptogamia  (N.  214)  ;  in  the 
torrid  zone  they  scarcely  form  one-twentieth,  and  in 
Lapland  one-thirtieth  part.  In  approaching  the  equa- 
tor, the  ligneous  exceed  the  number  of  herbaceous 
plants,  in  America  there  are  a  hundred  and  twenty 
different  species  of  forest  trees,  whereas  in  the  same 
latitudes  in  Europe  only  thirty-four  are  to  be  found. 

Similar  laws  appear  to  regulate  the  distribution  of 
marine  plants.  M.  Lamouroux  has  discovered  that  the 
groups  of  algae,  or  marine  plants,  affect  particular  tem- 
peratures or  zones  of  latitude,  though  some  few  genera 
prevail  throughout  the  ocean.  The  polar  Atlantic  basin, 
to  the  40th  degree  of  north  latitude,  presents  a  well-de- 
fined vegetation.  The  West  Indian  seas,  including  the 
Gulf  of  Mexico,  the  eastern  coast  of  South  America,  the 
Indian  Ocean  and  its  gulfs,  the  shores  of  New  Holland, 
and  the  neighboring  islands,  have  each  their  distinct 
species.  The  Mediterranean  possesses  a  vegetation 
peculiar  to  itself,  extending  to  the  Black  Sea ;  and  the 
species  of  marine  plants  on  the  coast  of  Sj^ia  and  in 
the  port  of  Alexandria  differ  almost  entirely  from  those 
of  Suez  and  the  Red  Sea,  notwithstanding  the  proxim- 
ity of  their  geographical  situation.  It  is  observed  that 
shallow  seas  have  a  different  set  of  plants  from  such  as 
are  deeper  and  colder;  and,  like  terrestrial  vegetation, 
the  algae  are  most  numerous  toward  the  equator,  where 
the  quantity  must  be  prodigious,  if  we  may  judge  from 
the  gulf-weed,  which  certainly  has  its  origin  in  the 
tropical  seas,  and  is  drifted,  though  not  by  the  gulf- 
stream,  to  higher  latitudes,  where  it  accumulates  in  such 
quantities,  that  the  early  Portuguese  navigators,  Colum- 


268  DISTRIBUTION  OF  MARINE  PLANTS.   SECT.  XXVII. 

bus  and  Lerius,  compared  the  sea  to  extensively  inun- 
dated meadows,  in  which  it  actually  impeded  their  ships 
and  alarmed  their  sailors.  M.  de  Humboldt,  in  his 
Personal  Narrative,  mentions  that  the  most  extensive 
bank  of  sea-weed  is  in  the  northern  Atlantic,  a  little 
west  of  the  meridian  of  Fayal,  one  of  the  Azores,  be- 
tween the  25th  and  36th  degrees  of  latitude.  Vessels 
returning  to  Europe  from  Monte  Video,  or  from  the 
Cape  of  Good  Hope,  cross  this  bank  nearly  at  an  equal 
distance  from  the  Antilles  and  Canary  Islands.  The 
other  bank  occupies  a  smaller  space,  between  the  22d 
and  26th  degrees  of  north  latitude,  about  eighty  leagues 
west  of  the  meridian  of  the  Bahama  Islands,  and  is  gen- 
erally traversed  by  vessels  on  their  passage  from  the 
Caicos  to  the  Bermuda  Islands.  These  masses  consist 
chiefly  of  one  or  two  species  of  Sargassum,  the  most  ex- 
tensive genus  of  the  order  Fucoideae. 

Some  of  the  sea- weeds  grow  to  the  enormous  length 
of  several  hundred  feet,  and  all  are  highly  colored, 
though  many  of  them  must  grow  in  the  deep  caverns  of 
the  ocean,  in  total  or  almost  total  darkness ;  light  how- 
ever may  not  be  the  only  principle  on  which  the  color  of 
vegetables  depends,  since  M.  de  Humboldt  met  with 
green  plants  growing  in  complete  darkness  at  the  bottom 
of  one  of  the  mines  at  Freyberg. 

It  appears  that  in  the  dark  and  tranquil  caves  of  the 
ocean,  on  the  shores  alternately  covered  and  deserted  by 
the  restless  waves,  on  the  lofty  mountain  and  extended 
plain,  in  the  chilly  regions  of  the  north  and  in  the  genial 
warmth  of  the  south,  specific  diversity  is  a  general  law 
of  the  vegqjplble  kingdom,  which  cannot  be  accounted  for 
by  diversity  of  climate  :  and  yet  the  similarity,  though 
not  identity,  of  species  is  such,  under  the  same  isother- 
mal lines,  that  if  the  number  of  species  belonging  to  one 
of  the  great  families  of  plants  be  known  in  any  part  of 
the  globe,  the  whole  number  of  the  phanerogamous  or 
more  perfect  plants,  and  also  the  number  of  species  com- 
posing the  other  vegetable  families,  may  be  estimated 
with  considerable  accuracy. 

Various  opinions  have  been  formed  on  the  original  or 
primitive  distribution  of  plants  over  the  surface  of  the 
globe  ;  but  since  botanical  geography  became  a  regular 


SKCT.  XXVH.        DISTRIBUTION  OF  ANIMALS.  269 

science,  the  phenomena  observed  have  led  to  the  con- 
clusion that  vegetable  creation  must  have  taken  place  in 
a  number  of  distinctly  different  centers,  each  of  which 
was  the  original  seat  of  a  certain  number  of  peculiar 
species,  which  at  first  grew  there  and  nowhere  else. 
Heaths  are  exclusively  confined  to  the  Old  World,  and 
no  indigenous  rose-tree  has  ever  been  discovered  in  the 
New;  the  whole  southern  hemisphere  being  destitute 
of  that  beautiful  and  fragrant  plant.  But  this  is  still 
more  confirmed  by  multitudes  of  particular  plants  hav- 
ing an  entirely  local  and  insulated  existence,  growing 
spontaneously  in  some  particular  spot  and  in  no  other 
place  ;  for  example,  the  cedar  of  Lebanon,  which  grows 
indigenously  on  that  mountain,  and  in  no  other  part  of 
the  world.  On  the  other  hand,  as  there  can  be  no  doubt 
but  that  many  races  of  plants  have  been  extinguished, 
Sir  John  Herschel  thinks  it  possible  that  these  solitary 
instances  may  be  the  last  surviving  remnants  of  the 
same  groups  universally  disseminated,  but  in  course  of 
extinction ;  or  that  perhaps  two  processes  may  be  going 
on  at  the  same  time ;  "  some  groups  may  be  spreading 
from  their  foci,  others  retreating  to  their  last  strong- 
holds." 

The  same  laws  obtain  in  the  distribution  of  the  ani- 
mal creation.  The  zoophyte  (N.  215),  occupying  the 
lowest  place  in  animated  nature,  is  widely  scattered 
through  the  seas  of  the  torrid  zone,  each  species  being 
confined  to  the  district  best  fitted  to  its  existence. 
Shell-fish  decrease  in  size  and  beauty  with  their  dis- 
tance from  the  equator ;  and  as  far  as  is  known,  each 
sea  has  its  own  kind,  and  every  basin  of  thelpean  is  in- 
habited by  its  peculiar  tribe  of  fish.  Indeed  MM.  Peron 
and  Le  Sueur  assert,  that  among  the  many  thousands 
of  marine  animals  which  they  had  examined,  there  is 
not  a  single  animal  of  the  southern  regions  which  is  not 
distinguishable  by  essential  characters  from  the  analo- 
gous species  in  the  northern  seas.  Reptiles  are  not 
exempt  from  the  general  law.  The  saurian  (N.  216) 
tribes  of  the  four  quarters  of  the  globe  differ  in  species ; 
and  although  warm  countries  abound  in  venomous 
snakes,  they  are  specifically  different,  and  decrease  both 
in  numbers  and  in  the  virulence  of  their  poison  with  de- 


270  MANKIND  IDENTICAL  IN  SPECIES.   SECT.  XXVII. 

crease  of  temperature.  The  dispersion  of  insects  ne- 
cessarily follows  that  of  the  vegetables  which  supply 
them  with  food  ;  and  in  general  it  is  observed,  that  each 
kind  of  plant  is  peopled  by  its  peculiar  inhabitants. 
Each  species  of  bird  has  its  particular  haunt,  notwith- 
standing the  locomotive  powers  of  the  winged  tribes. 
The  emu  is  confined  to  Australia,  the  condor  never 
leaves  the  Andes,  nor  the  great  eagle  the  Alps ;  and 
although  some  birds  are  common  to  every  country,  they 
are  few  in  number.  Quadrupeds  are  distributed  in  the 
same  manner  wherever  man  has  not  interfered.  Such 
as  are  indigenous  in  one  continent  are  not  the  same  with 
their  congeners  in  another ;  and  with  the  exception  of 
some  kinds  of  bats,  no  warm-blooded  animal  is  indigenous 
v  in  the  Polynesian  Archipelago,  nor  in  any  of  the  islands 
on  the  borders  of  the  central  part  of  the  Pacific. 

In  reviewing  the  infinite  variety  of  organized  beings 
that  people  the  surface  of  the  globe,  nothing  is  more  re- 
markable than  the  distinctions  which  characterize  the 
different  tribes  of  mankind,  from  the  ebony  skin  of  the 
torrid  zone  to  the  fair  and  ruddy  complexion  of  Scandi- 
navia— a  difference  which  existed  in  the  earliest  recorded 
times,  since  the  African  is  represented  in  the  Sacred 
Writings  to  have  been  as  black  as  he  is  at  the  present 
day,  and  the  most  ancient  Egyptian  paintings  confirm 
that  truth ;  yet  it  appears  from  a  comparison  of  the 
principal  circumstances  relating  to  the  animal  economy 
or  physical  character  of  the  various  tribes  of  mankind, 
that  the  different  races  are  identical  in  species.  Many 
attempts  have  been  made  to  trace  the  various  tribes 
back  to  ^•pommon  origin,  by  collating  the  numerous 
languages^vhich  are  or  have  been  spoken.  Some 
classes  of  these  have  few  or  no  words  in  common,  yet 
exhibit  a  remarkable  analogy  in  the  laws  of  their  gram- 
matical construction.  The  languages  spoken  by  the 
native  American  nations  afford  examples  of  these ;  in- 
deed the  refinement  in  the  grammatical  construction  of 
the  tongues  of  the  American  savages  leads  to  the  belief, 
that  they  must  originally  have  been  spoken  by  a  much 
more  civilized  class  of  mankind.  Some  tongues  have 
little  or  no  resemblance  in  structure,  though  they  cor- 
respond extensively  in  their  vocabularies,  as  the  Syrian 


SKCT.  XXV1U.     INFLUENCE  OF  ELECTRICITY.  271 

dialects.  In  all  of  these  cases  it  may  be  inferred,  that 
the  nations  speaking  the  languages  in  question  are  de- 
scended from  the  same  stock ;  but  the  probability  of  a 
common  origin  is  much  greater  in  the  Indo-European 
nations,  whose,  languages,  such  as  the  Sanscrit,  Greek, 
Latin,  German,  &c.,  have  an  affinity  both  in  structure 
and  correspondence  of  vocables.  In  many  tongues*  not 
the  smallest  resemblance  can  be  traced  ;  length  of  time, 
however,  may  have  obliterated  origiAd  -identity.  The 
conclusion  drawn  from  the  whole  investigation  is,  that 
although  the  distribution  of  organized  beings  does  not 
follow  the  direction  of  the  isothermal  lines,  temperature 
has  a  very  great  influence  on  their  physical  development. 
The  heat  of  the  air  is  so  intimately  connected  with  its 
electrical  condition,  that  electricity  must  also  affect  the 
distribution  of  plants  and  animals  over  the  face  of  the 
earth,  the  more  so  as  it  seems  to  have  a  great  share  in 
the  functions  of  animal  and  vegetable  life.  It  is  the  sole 
cause  of  many  atmospheric  and  terrestrial  phenomena, 
and  performs  an  important  part  in  the  economy  of  nature. 


SECTION  XXVIII. 

Of  ordinary  Electricity,  generally  called  Electricity  of  Tension — Methods 
of  exciting  Bodies— Transference — Electrics  and  Non-Electrics—Law  of 
its  Intensity— Distribution — Tension — Electric  Heat  and  Light — Atmos- 
pheric Electricity— Its  Cause — Electric  Clouds— Back  Stroke— Violent 
Effects  of  Lightning — Its  Velocity— Phosphorescence — Phosphorescent 
Action  of  Solar  Spectrum — Aurora. 

ELECTRICITY  is  one  of  those  imponderable  agents 
pervading  the  earth  and  all  substances,  witl^lt  affecting 
their  volume  or  temperature,  or  even  givin^my  visible 
sign  of  its  existence  when  in  a  latent  state ;  but  when 
elicited  developing  forces  capable  of  producing  the  most 
sudden,  violent,  and  destructive  effects  in  some  cases, 
while  in  others  their  action,  though  less  energetic,  is  of 
indefinite  and  uninterrupted  continuance.  These  modi- 
fications of  the  electric  force,  incidentally  depending 
upon  the  manner  in  which  it  is  excited,  present  phe- 
nomena of  great  diversity,  but  yet  so  connected  as  to 
justify  the  conclusion  that  they  originate  in  a  common 
principle. 


272  ELECTRICS. 

Electricity  may  be  called  into  activity  by  mechanical 
power,  by  chemical  action,  by  heat,  and  by  magnetic 
influence.  We  are  totally  ignorant  why  it  is  roused 
from  its  neutral  state  by  such  means,  or  of  the  manner 
of  its  existence  in  bodies,  whether  it  be  a-material  agent, 
vibrations  of  ether,  or  merely  a  property  of  matter. 
Various  circumstances  render  it  more  than  probable 
that,  like  light  and  heat,  it  is  a  modification  or  vibration 
of  that  subtile  etlftreaT  medium  which  in  a  highly  elas- 
tic state  pervades  all  space,  and  which  is  capable  of 
moving  with  various  degrees  of  facility  through  the  pores 
even  of  the  densest  substances.  As  experience  shows 
that  bodies  in  one  electric  state  attract,  and  in  another 
repel  each  other,  the  hypothesis  of  two  fluids  has  been 
adopted  by  many  philosophers  ;  but  probably  the  mutual 
attraction  and  repulsion  of  bodies  arise  from  the  redun- 
dancy and  defect  of  their  electricities,  though  all  the 
electrical  phenomena  can  be  explained  on  either  hy- 
pothesis. Bodies  having  a  redundancy  of  the  electric 
fluid  are  said  to  be  positively  electric,  and  those  in  defect 
negatively.  As  each  kind  of  electricity  has  its  peculiar 
properties,  the  science  may  be  divided  into  four  branch- 
es, of  which  the  following  notice  is  intended  to  convey 
some  idea. 

Substances  in  a  neutral  state  neither  attract  nor 
repel.  There  is  a  numerous  class  called  electrics, 
in  which  the  electric  equilibrium  is  destroyed  by  fric- 
tion ;  then  the  positive  and  negative  electricities  are 
called  into  action  or  separated ;  the  positive  is  im- 
pelled in  one  direction,  and  the  negative  in  another ; 
or  more  jflfcrectly,  the  electricity  is  impelled  in  one  di- 
rection, at^ie  expense  of  the  other  where  there  is  a  de- 
ficiency of  it.  .Electricities  of  the  same  kind  repel, 
whereas  those  of  different  kinds  attract  each  other. 
The  attractive  power  is  exactly  equal  to  the  repulsive 
power  at  equal  distances,  and  when  not  opposed,  they 
coalesce  .with  great  rapidity  and  violence;  producing 
the  electric  flash,  explosion,  and  shock :  then  equili- 
brium is  restored,  and  the  electricity  remains  latent  till 
again  called  forth  by  a  new  exciting  cause.  One  kind 
of  electricity  cannot  be  evolved  without  the  evolution  of 
an  equal  quantity  of  the  opposite  kind.  Thus  when  u 


SECT.  XXVIII.  NON-ELECTRICS.  273 

glass  rod  is  rubbed  with  a  piece  of  silk,  as  much  positive 
electricity  is  elicited  in  the  glass  as  there  is  negative  in 
the  silk  ;  or  in  other  words  there  is  a  redundancy  in  the 
glass  and  a  proportional  deficiency  in  the  silk.  The 
kind  of  electricity  depends  more  upon  the  mechanical 
condition  than  on  the  nature  of  the  surface  :  for  when 
two  plates  of  glass,  one  polished  and  the  other  rough, 
are  rubbed  against  each  other,  the  polished  surface  ac- 
quires positive  and  the  rough  negative  electricity ;  that 
is,  the  one  gains  and  the  other  loses.  The  manner  in 
which  friction  is  performed  also  alters  the  kind  of  elec- 
tricity. Equal  lengths  of  black  and  white  riband  ap- 
plied longitudinally  to  one  another,  and  drawn  between 
the  finger  and  thumb,  so  as  to  rub  their  surfaces  to- 
gether, become  electric.  When  separated,  the  white 
riband  is  found  to  have  acquired  positive  electricity,  and 
the  black  has  lost  it,  or  become  negative :  but  if  the 
whole  length  of  the  black  riband  be  drawn  across  the 
breadth  of  the  white,  the  black  will  be  positively  and 
the  white  negatively  electric  when  separate.  Elec- 
tricity may  be  transferred  from  one  body  to  another  in 
the  same  manner  as  heat  is  communicated,  and  like  it 
too,  the  body  loses  by  the  transmission.  Although'  no 
substance  is  altogether  impervious  to  the  electric  fluid, 
nor  is  there  any  that  does  not  oppose  some  resistance 
to  its  passage,  yet  it  moves  with  much  more  facility 
through  a  certain  class  of  substances  called  conductors, 
such  as  metals,  water,  the  human  body,  &c.,  than 
through  atmospheric  air,  glass,  silk,  &c.,  which  are 
therefore  called  non-conductors.  The  conducing  power 
is  affected  both  by  temperature  and  moisture.^ 

Bodies  surrounded  with  non-conductors  are  said  to  be 
insulated,  because,  when  charged,  the  electricity  cannot 
escape.  When  that  is  not  the  case,  the  electricity  is 
conveyed  to  the  earth,  which  is  formed  of  conducting 
matter;  consequently  it  is  impossible  to  accumulate 
electricity  in  a  conducting  substance  that  is  not  insu- 
lated. There  are  a  great  many  substances  called  non- 
electrics,  in  which  electricity  is  not  sensibly  developed 
by  friction,  unless  they  be  insulated,  probably  because  it 
is  carried  off  by  their  conducting  power  as  soon  as 
elicited.  Metals,  for  example,  which  are  said  to  be 
18 


274  ELECTRICAL  FORCES.  SECT.  XXVIII. 

non-electrics,  can  be  excited,  but  being  conductors,  they 
cannot  retain  this  state  if  in  communication  with  the 
earth.  It  is  probable  that  no  bodies  exist  which  are 
either  perfect  non-electrics  or  perfect  non-conductors. 
But  it  is  evident  that  electrics  must  be  non-conductors 
to  a  certain  degree,  otherwise  they  could  not  retain 
their  electric  state. 

It  has  been  supposed  that  an  insulated  body  remains 
at  rest,  because  the  tension  of  the  electricity,  or  its  pres- 
sure on  the  air  which  restrains  it,  is  equal  on  all  sides ; 
but  when  a  body  in  a  similar  state,  and  charged  with 
the  same  kind  of  electricity,  approaches  it,  that  the  mu- 
tual repulsion  of  the  particles  of  the  electric  fluid  di- 
minishes the  pressure  of  the  fluid  on  the  air  on  the 
adjacent  sides  of  the  two  bodies,  and  increases  it  on 
their  remote  ends ;  consequently  that  equilibrium  will 
be  destroyed,  and  the  bodies,  yielding  to  the  action  of 
the  preponderating  force,  will  recede  from  or  repel 
each  other.  When,  on  the  contrary,  they  are  charged 
with  opposite  electricities,  it  is  alleged  that  the  pressure 
upon  the  air  on  the  adjacent  sides  will  be  increased  by 
the  mutual  attraction  of  the  particles  of  the  electric 
fluid,  and  that  on  the  further  sides  diminished ;  con- 
sequently, that  the  force  will  urge  the  bodies  toward 
one  another,  the  motion  in  both  cases  corresponding  to 
the  forces  producing  it.  An  attempt  has  thus  been 
made  to  attribute  electrical  attractions  and  repulsions  to 
the  mechanical  pressure  of  the  atmosphere.  It  is  more 
than  doubtful,  however,  whether  these  phenomena  can 
be  referijgpl  to  that  cause ;  but  certain  it  is,  that  what- 
ever theTiature  of  these  forces  may  be,  they  are  not 
impeded  in  their  action  by  the  intervention  of  any  sub- 
stance whatever,  provided  it  be  not  itself  in  an  electric 
state. 

A  body  charged  with  electricity,  although  perfectly 
insulated,  so  that  all  escape  of  electricity  is  precluded, 
tends  to  produce  an  electric  state  of  the  opposite  kind 
in  all  bodies  in  its  vicinity.  Positive  electricity  tends 
to  produce  negative  electricity  in  a  body  near  to  it,  and 
vice  versa,  the  effect  being  greater  as  the  distance  di- 
minishes. This  power  which  electricity  possesses,  of 
causing  an  opposite  electrical  state  in  its  vicinity,  is  called 


S«cr.  XXVllf.  ELECTRICAL  FORCES.  275 

induction.  When  a  body  in  either  electric  state  is  pre- 
sented to  a  neutral  one,  its  tendency,  in  consequence  of 
the-  law  of  induction,  is  to  disturb  the  electrical  condi- 
tion of  the  neutral  body.  The  electrified  body  induces 
electricity  contrary  to  its  own  in  the  adjacent  part  of 
the  neutral  one,  and  therefore  an  electrical  state  similar 
to  its  own  in  the  remote  part.  Hence  the  neutrality  of 
the  second  body  is  destroyed  by  the  action  of  the  first, 
and  the  adjacent  parts  of  the  two,  having  now  opposite 
electricities,  will  attract  each  other.  The  attraction  be- 
tween electrified  and  unelectrified  substances  is,  there- 
fore, merely  a  consequence  of  their  altered  state,  re- 
sulting directly  from  the  law  of  induction,  and  not  an 
original  law.  The  effects  of  induction  depend  upon  the 
facility  with  which  the  equilibrium  of  the  neutral  state 
of  a  body  can  be  overcome — a  facility  which  is  propor- 
tional to  the  conducting  power  of  the  body.  Conse- 
quently the  attraction  exerted  by  an  electrified  substance 
upon  another  substance  previously  neutral,  will  be  much 
more  energetic  if  the  latter  be  a  conductor  than  if  it  be 
a  non-conductor. 

The  law  of  electrical  attraction  and  repulsion  has 
been  determined  by  suspending  a  needle  of  gum-lac 
horizontally  by  a  silk  fibre,  the  needle  carrying  at  one 
end  a  piece  of  electrified  gold-leaf.  A  globe  in  the  same, 
or  in  the  opposite  electrical  state,  when  presented  to 
the  gold  leaf,  will  repel  or  attract  it,  and  will  therefore 
cause  the  needle  to  vibrate  more  or  less  rapidly  accord- 
ing to  the  distance  of  the  globe.  A  comparison  of  the 
number  of  oscillations  performed  in  a  given  lime  at  dif- 
ferent distances,  will  determine  the  law  of  the  variation 
of  the  electrical  intensity,  in  the  same  manner  that  the 
force  of  gravitation  is  measured  by  the  oscillations  of 
the  pendulum.  Coulomb  invented  an  instrument  which 
balances  the  forces  in  question  by  the  force  of  the  tor- 
sion of  a  thread,  which  consequently  measures  their 
intensity  ;  and  Mr.  Snow  Harris  has  recently  construct- 
ed an  instrument  with  which  he  has  measured  the 
intensity  of  the  electrical  force  in  terms  of  the  weight 
requisite  to  balance  it.  By  these  methods  it  has  been 
found  that  the  intensity  of  the  electrical  attraction  and 
repulsion  varies  inversely  as  the  squares  of  the  distances. 


276  ELECTRICAL  INDUCTION.          SECT.  XXV11I. 

However,  the  law  of  the  repulsive  force  is  liable  to  great 
disturbance  from  inductive  action,  which  Mr.  Snow  Har- 
ris has  found  to  exist  not  only  between  a  charged  and 
neutral  body,  but  also  between  bodies  similarly  charged, 
and  that  in  the  latter  case  the  inductive  process  may  be- 
indefinitely  modified  by  the  various  circumstances  of  the 
quantity  and  intensity  of  the  electricity,  and  the  distance 
between  the  charged  bodies.  Since  electricity  can  only 
be  in  equilibrio  from  the  mutual  repulsion  of  its  par- 
ticles, which  according  to  these  experiments  varies  in- 
versely as  the  square  of  the  distances,  its  distribution  in 
different  bodies  depends  upon  the  laws  of  mechanics, 
and  therefore  becomes  a  subject  of  analysis  and  calcula- 
tion. Although  the  distribution  of  the  electric  fluid  has 
employed  the  eminent  analytical  talents  of  M.  Poisson 
and  Mr.  Ivory,  and  though  many  of  their  computed 
phenomena  have  been  confirmed  by  observation,  yet 
recent  experiments  show  that  the  subject  is  still  involved 
in  much  difficulty.  Electricity  is  entirely  confined  to 
the  surface  of  bodies ;  or  if  it  does  penetrate  their  sub- 
stance, the  depth  is  inappreciable  ;  so  that  the  quantity 
bodies  are  capable  of  receiving  does  not  follow  the  pro- 
portion of  their  bulk,  but  depends  principally  upon  the 
form  and  extent  of  surface  over  which  it  is  spread  :  thus 
the  exterior  may  be  positively  or  negatively  electric, 
while  the  interior  is  in  a  state  of  perfect  neutrality. 

It  appears  from  the  experiments  of  Mr.  Snow  Harris, 
that  a  given  quantity  of  electricity  divided  between  two 
perfectly  equal  and  similar  bodies,  exerts  upon  external 
bodies  only  one-fourth  of  the  attractive  force  apparent 
when  disposed  upon  one  of  them  ;  and  if  it  be  distrib- 
uted among  three  equal  and  similar  bodies,  the  force  is 
one-ninth  of  that  apparent  when  it  is  disposed  on  one  of 
them.  Hence  if  the  quantity  of  electricity  be  the  same, 
the  force  varies  inversely  as  the  square  of  the  surface 
over  which  it  is  disposed  ;  and  if  the  surface  be  the  same, 
the  force  varies  directly  as  the  square  of  the  quantity 
of  the  electric  fluid.  These  laws  however  do  not  hold 
when  the  form  of  the  surface  is  changed.  A  given 
quantity  of  electricity  disposed  on  a  given  surface  has  the 
greatest  intensity  when  the  surface  has  a  circular  form, 
and  the  least  intensity  when  the  surface  is  expanded 


S«cr.  XXVIII.          ELECTRICAL  INTENSITY.  277 

into  an  indefinite  right  line.  The  decrease  of  intensity 
seems  to  arise  from  some  peculiar  arrangement  of  the 
electricity  depending  on  the  extension  of  the  surface, 
and  has  been  considered  by  Volta  to  consist  in  the  re- 
moval of  the  electrical  particles  farther  without  the 
sphere  of  each  other's  influence.  It  i's  quite  independ- 
ent of  the  extent  of  the  edge,  the  area  being  the  same  ; 
for  Mr.  Snow  Hams  found  that  the  electrical  intensity 
of  a  charged  sphere  is  the  same  with  that  of  a  plane 
circular  area  of  the  same  superficial  extent,  and  that  of 
a  charged  cylinder  the  same  as  if  it  were  cut  open  and 
expanded  into  a  plane  surface. 

The  same  able  electrician  has  shown  that  the  attract- 
ive force  between  an  electrified  and  a  neutral  uninsulated 
body  is  the  same,  whatever  be  the  forms  of  their  unop- 
posed parts.  Thus  two  hemispheres  attract  each  other 
with  precisely  the  same  force  as  if  they  were  spheres ; 
and  as  the  force  is  as  the  number  of  attracting  points  in 
operation  directly,  and  as  the  squares  of  the  respective 
distances  inversely,  it  follows  that  the  attraction  between 
a  mere  ring  and  a  circular  area  is  no  greater  than  that 
between  two  similar  rings,  and  the  force  between  a 
sphere  and  an  opposed  spherical  segment  of  the  same 
curvature  is  no  greater  than  that  of  two  similar  segments, 
each  equal  to  the  given  segment. 

Electricity  may  be  accumulated  to  a  great  extent  in 
insulated  bodies :  and  so  long  as  it  is  quiescent,  it  occa- 
sions no  sensible  change  in  their  properties,  though  it  is 
spread  over  their  surfaces  in  indefinitely  thin  layers. 
When  restrained  by  the  non-conducting  power  of  the 
atmosphere,  the  tension  or  pressure  exerted  by  the  elec- 
tric fluid  against  the  air  which  opposes  its  escape,  is  in 
the  ratio  compounded  of  the  repulsive  force  of  its  own 
particles  at  the  surface  of  the  stratum  of  the  fluid,  and 
of  the  thickness  of  that  stratum.  But  as  one  of  these 
elements  is  always  proportional  to  the  other,  the  total 
pressure  on  eveiy  point  must  be  proportional  to  the 
squares  of  the  thickness.  'If  this  pressure  be  less  than 
the  coercive  force  of  the  ah*,  the  electricity  is  retained ; 
but  the  instant  it  exceeds  that  force  in  any  one  point, 
the  electricity  escapes,  which  it  will  do  when  the  air  is 
attenuated,  or  becomes  saturated  with  moisture.  '  Tt  ap- 
A  A 


278  ELECTRICAL  INTENSITY.          SECT.  XXVIII. 

pears  that  the  resistance  of  the  air  to  the  passage  of  the 
electric  fluid  is  proportional  to  the  square  of  its  density, 
but  that  the  action  of  electricity  on  distant  bodies  by  in- 
duction is  quite  independent  of  atmospheric  pressure, 
and  is  the  same  in  vacuo  as  in  air. 

The  power  of  retaining  electricity  depends  also  upon 
the  shape  of  the  body.  It  is  most  easily  retained  by  a 
sphere,  next  to  that  by  a  spheroid,  but  it  readily  escapes 
from  a  point;  and  a  pointed  object  receives  it  with 
most  facility.  It  appears  from  analysis,  that  electricity, 
when  in  equilibrio,  spreads  itself  in  a  thin  stratum  over 
the  surface  of  a  sphere,  in  consequence  of  the  repulsion 
of  its  particles,  which  force  is  directed  from  the  center 
to  the  surface.  In  an  oblong  spheroid,  the  intensity  or 
thickness  of  the  stratum  of  electricity  at  the  extremities 
of  the  two  axes  is  exactly  in  the  proportion  of  the  axes 
themselves ;  hence,  when  the  ellipsoid  is  much  elon- 
gated, the  electricity  becomes  very  feeble  at  the  equator, 
and  powerful  at  the  poles.  A  still  greater  difference  in 
the  intensities  takes  place  in  bodies  of  cylindrical  or 
prismatic  form,  and  the  more  so  in  proportion  as  their 
length  exceeds  their  breadth ;  therefore  the  electrical 
intensity  is  very  powerful  at  a  point  where  nearly  the 
whole  electricity  in  the  body  is  concentrated.  Not- 
withstanding these  analytical  results,  it  is  doubted 
whether  the  disposition  of  electrified  bodies  to  discharge 
their  electricity  from  points  or  edges  may  not  arise  from 
the  superior  attractive  force  generated  by  induction  in 
external  bodies,  rather  than  from  an  original  concentra- 
tion of  the  electric  fluid  in  these  parts. 

A  perfect  conductor  is  not  mechanically  affected  by 
the  passage  of  electricity,  if  it  be  of  sufficient  size  to 
carry  off  the  whole  ;  but  it  is  shivered  to  pieces  in  an 
instant  if  it  be  too  small  to  carry  off  the  charge  :  this 
also  happens  to  a  bad  conductor.  In  that  case  the 
physical  change  is  generally  a  separation  of  the  particles, 
though  it  may  occasionally  be  attributed  to  chemical 
action,  or  expansion  from  the  heat  evolved  during  the 
passage  of  the  fluid ;  but  all  these  effects  are  in  propor- 
tion to  the  obstacles  opposed  to  the  freedom  of  its 
course.  The  heat  produced  by  the  electric  shock  is 
intense,  fusing  metals,  and  even  volatilizing  substances, 


Ill 

,: 

to 


SECT.  XXVIII.  ELECTRICAL  LIGHT.  279 

though  it  is  only  accompanied  by  light  when  the  fluid  is 
obstructed  in  its  passage. 

Electrical  light,  when  analyzed  by  the  prism,  pre- 
sents very  different  appearances  to  the  solar  light. 
Frauenhofer  found  that  instead  of  the  fixed  dark  lines 
of  the  solar  spectrum,  the  spectrum  of  an  electric  spark 
was  crossed  by  very  numerous  bright  lines ;  and  Pro- 
fessor Wheatstone  has  observed  that  the  number  and 
position  of  the  lines  differ  with  the  metal  from  which 
the  spark  is  taken.  According  to  M.  Biot,  electrical 
light  arises  from  the  condensation  of  the  air  during  the 
rapid  motion  of  the  electricityr  and  varies  both  in  in- 
tensity and  color  with  the  density  of  the  atmosphere. 
When  the  air  is  dense,  it  is  white  and  brilliant;  whereas 
in  rarefied  air  it  is  diffuse  and  of  a  reddish  color.  The 
experiments  of  Sir  Humphiy  Davy,  however,  seem  to 
be  at  variance  with  this  opinion.  He  passed  the  elec- 
tric spark  through  a  vacuum  over  mercury,  which, 
from  green,  became  successively  sea-green,  blue,  and 
purple,  on  admitting  different  quantities  of  air.  When 
the  vacuum  was  made  over  a  fusible  alloy  of  tin  and 
bismuth,  the  spark  was  yellowish  and  extremely  pale. 
Sir  Humphry  thence  concluded,  that  electrical  light 
principally  depends  upon  some  properties  belonging  to 
the  ponderable  matter  through  which  it  passes,  and 
that  space  is  capable  of  exhibiting  luminous  appearances, 
though  it  does  not  contain  an  appreciable  quantity  of 
this  matter.  He  thought  it  not  improbable  that  the 
superficial  particles  of  bodies  which  form  vapor,  when 
detached  by  the  repulsive  power  of  heat,  might  be 
equally  separated  by  the  electric  forces,  and  produce 
luminous  appearances  in  vacuo,  by  the  destruction  of 
their  opposite  electric  states.  Professor  Wheatstone 
has  been  led  to  conclude  that  electrical  light  results 
from  the  volatilization  and  ignition  of  the  ponderable 
matter  of  the  conductor  itself. 

Pressure  is  a  source  of  electricity  which  M.  Becquerel 
has  found  to  be  common  to  all  bodies  ;  but  it  is  necessary 
to  insulate  them  to  prevent  its  escape. J  When  two  sub- 
stances of  any  kind  whatever  are  insulated  and  pressed 
together,  they  assume  different  electric  states,  but  they 
only  show  contrary  electricities  when  one  of  them  is  a 


280  SOURCES  OF  ELECTRICITY.        SECT.  XXVIII. 

good  conductor.  When  both  are  good  conductors,  they 
must  be  separated  with  extreme  rapidity,  to  prevent 
the  return  to  equilibrium.  /When  the  separation  is 
very  sudden,  the  tension  of  the  two  electricities  may  be 
great  enough  to  produce  light. ;  M.  Becquerel  attributes 
the  light  produced  by  the  collision  of  icebergs  to  this 
cause.  Iceland  spar  is  made  electric  by  the  smallest 
pressure  between  the  finger  and  thumb,  and  retains  it 
for  a  long  time.  All  these  circumstances  are  modified 
by  the  temperature  of  the  substances,  the  state  of  their 
surfaces,  and  that  of  the  atmosphere.  Several  crys- 
taline  substances  become  electric  when  heated,  es- 
pecially tourmaline,  one  end  of  which  acquires  positive 
and  the  other  negative  electricity,  while  the  interme- 
diate partis  neutral.  If  a  tourmaline  be  broken  through 
the  middle,  each  fragment  is  found  to  possess  positive 
electricity  at  one  encH  and  negative  at  the  other,  like 
the  entire  crystal.  Electricity  is  evolved  by  bodies 
passing  from  a  liquid  to  a  solid  state ;  also  by  chemical 
action  during  the  production  and  condensation  of  vapor, 
which  is  consequently  a  great  source  of  atmospheric 
electricity.  The  steam  issuing  from  the  valve  of  an 
insulated  locomotive  steam  engine  produces  seven  times 
the  quantity  of  electricity  that  an  electrifying  machine 
would  do  with  a  plate  three  feet  in  diameter,  and 
worked  at  the  rate  of  70  revolutions  in  a  minute.)  In 
short,  it  may  be  stated  generally,  that  when  any  <4use 
whatever,  such  as  friction,  pressure,  heat,  fracture, 
chemical  action,  &c.,  tends  to  destroy  molecular  attrac- 
tion, there  is  a  development  of  electricity.  If,  however, 
the  molecules  be  not  immediately  separated,  there  will 
be  an  instantaneous  restoration  of  equilibrium. 

The  earth  possesses  a  powerful  electrical  tension,  and 
the  atmosphere,  when  clear,  is  almost  always  positively 
electric.  Its  electricity  is  stronger  in  winter  than  in 
summer,  during  the  day  than  in  the  night.  The  inten- 
sity increases  for  two  or  three  hours  from  the  time  of 
sunrise,  comes  to  a  maximum  between  seven  and  eight, 
then  decreases  toward  the  middle  of  the  day,  arrives  at 
its  minimum  between  one  and  two,  and  again  augments 
as  the  sun  declines,  till  about  the  time  of  sunset,  after 
which  it  diminishes,  and  continues  feeble  during  the 


SKCT.  XXVni.      ATMOSPHERIC  ELECTRICITY.  281 

night,/  Atmospheric  electricity  arises  partly  from  an 
evolution  of  the  electric  fluid  during  the  evaporation 
that  is  so  abundant  at  the  surface  of  the  earth,  though 
not  under  all  circumstances.  M.  Pouillet  has  recently 
come  to  the  conclusion,  that  simple  evaporation  never 
produces  electricity,  unless  accompanied  by  chemical 
action,  but  that  electricity  is  always  disengaged  when 
the  water  holds  a  salt  or  some  other  substance  in  solu- 
tion, f  He  found  when  water  contains  lime,  chalk,  or 
any  solid  alkali,  that  the  vapor  arising  from  it  is  nega- 
tively electric ;  and  when  the  body  held  in  solution  is 
either  gas,  acid,  or  some  of  the  salts,  that  the  vapor 
given  out  is  positively  electric.  /  The  ocean  must  there- 
fore afford  a  great  supply  of"positive  electricity  to  the 
atmosphere  ;  but  as  M.  Becquerel  has  shown  that  elec- 
tricity of  one  kind  or  other  is  developed,  whenever  the 
molecules  of  bodies  are  deranged  from  their  natural 
positions  of  equilibrium  by  any  cause  whatever,  the 
chemical  changes  on  the  surface  of  the  globe  must  occa- 
sion many  variations  in  the  electrical  state  of  the  atmos- 
phere. 

Clouds  probably  owe  their  existence,  or  at  least  their 
form,  to  electricity,  for  according  to  some  authors  they 
consist  of  hollow  vesicles  of  vapor  coated  with  it.  As 
the  electricity  is  either  entirely  positive  or  negative,  the 
vesicles  repel  each  other,  which  prevents  them  from 
uniting  and  falling  down  in  rain.  The  friction  of  the 
surfaces  of  two  gjrata  of  air  moving  in  different  direc- 
tions, probably  developes  electricity;  and  if  the  strata 
be  of  different  temperatures,  a  portion  of  the  vapor  they 
always  contain  will  be  deposited  ;  the  electricity  evolved 
will  be 'taken  up  by  the  vapor,  and  cause  it  to  assume 
the  vesicular  state  constituting  a  cloud.  A  vast  deal  of 
electricity  may  be  accumulated  in  this  manner,  which 
may  be  either  positive  or  negative.  When  two  clouds, 
charged  with  opposite  kinds,  approach  within  a  certain 
distance,  the  thickness  of  the  coating  of  electricity  in- 
creases on  the  two  sides  of  the  clouds  that  are  nearest 
to  one  another;  and  when  the  accumulation  becomes 
so  great  as  to  overcome  the  coercive  pressure  of  the 
atmosphere,  a  discharge  takes  place,  which  occasions  a 
flash  of  lightning.  The  actual  quantity  of  electricity  in 

AA2 


282  ELECTRIC  CLOUDS.  .  SECT.  XXVIII. 

any  one  part  of  a  cloud  is  extremely  small.  The  inten- 
sity of  the  flash  arises  from  the  very  great  extent  of 
surface  occupied  by  the  electricity;  so  that  clouds  may 
be  compared  to  enormous  Leyden  jars  thinly  coated 
with  the  electric  fluid,  which  only  acquires  its  intensity 
by  its  instantaneous  condensation.  The  rapid  and  irreg- 
ular motions  of  thunder  clouds  are,  in  all  probability, 
more  owing  to  strong  electrical  attractions  and  repul- 
sions among  themselves  than  to  currents  of  air,  though 
both  are  no  doubt  concerned  in  these  hostile  move- 
ments. 

Since  the  air  is  a  non-conductor,  it  does  not  convey 
the  electricity  from  the  clouds  to  the  earth,  but  it  ac- 
quires from  them  an  opposite  electricity,  and  when  the 
tension  is  very  great  the  force  of  the  electricity  becomes 
irresistible,  and  an  interchange  takes  place  between  the 
clouds  and  the  earth  ;  but  so  rapid  is  the  motion  of  light- 
ning, that  it  is  difficult  to  ascertain  when  it  goes  from  the 
clouds  to  the  earth,  or  shoots  upward  from  the  earth 
to  the  clouds,  though  there  can  be  no  doubt  that  it  does 
both.  In  a  storm  which  occurred  at  Manchester,  in  the 
month  of  June,  1835,  the  electric  fluid  was  observed  to 
issue  from  various  points  of  a  road,  attended  by  explo- 
sions as  if  pistols  had  been  fired  out  of  the  ground.  A 
man  appears  to  have  been  killed  by  one  of  these  explo- 
sions taking  place  under  his  right  foot.  M.  Gay-Lussac 
has  ascertained  that  a  flash  of  lightning  sometimes  darts 
more  than  three  miles  at  once  in  a  straight  line. 

A  person  may  be  killed  by  lightning,  although  the 
explosion  takes  place  at  the  distance  of  twenty  miles, 
by  what  is  called  the  back  stroke.  Suppose  that  the 
two  extremities  of  a  cloud  highly  charged  with  electri- 
city hang  down  toward  the  earth  :  they  will  repel  the 
electricity  from  the  earth's  surface,  if  it  be  of  the  same 
kind  with  their  own,  and  will  attract  the  other  kind ; 
and  if  a  discharge  should  suddenly  take  place  at  one 
end  of  the  cloud,  the  equilibrium  will  instantly  be  re- 
stored by  a  flash  at  that  point  of  the  earth  which  is  un- 
der the  other.  Though  the  back  stroke  is  often  suffi- 
ciently powerful  to  destroy  life,  it  is  never  so  terrible  in 
its  effects  as  the  direct  shock,  which  is  frequently  of 
inconceivable  intensity-  Instances  have  occurred  in 


SECT.  XXVIII.         LIGHTNING  CONDUCTORS.  283 

which  large  masses  of  iron  and  stone,  and  even  many 
feet  of  a  stone  wall,  have  been  conveyed  to  a  con- 
siderable distance  by  a  stroke  of  lightning.  Rocks  and 
the  tops  of  mountains  often  bear  the  marks  of  fusion 
from  its  action;  and  occasionally  vitreous  tubes,  de-« 
scending  many  feet  into  banks  of  sand,  mark  the  path 
of  the  electric  fluid.  Some  years  ago,  Dr.  Fiedler  ex- 
hibited several  of  these  fulgorites  in  London,  of  con- 
siderable length,  which  had  been  dug  out  of  the  sandy 
plains  of  Silesia  and  Eastern  Prussia.  One  found  at 
Paderborn  was  forty  feet  long.  Their  ramifications 
generally  terminate  in  pools  or  springs  of  water  below 
the  sand,  which  are  supposed  to  determine  the  course 
of  the  electric  fluid.  No  doubt  the  soil  and  substrata 
must  influence  its  direction,  since  it  is  found  by  experi- 
ence that  places  which  have  been  struck  by  lightning 
are  often  struck  again.  A  school-house  in  Lammer- 
muir,  East  Lothian,  has  been  struck  three  different 
times. 

The  atmosphere,  at  all  times  positively  electric,  be- 
comes intensely  so  on  the  approach  of  rain,  snow,  wind, 
hail,  or  sleet ;  but  it  afterward  varies,  and  the  transi- 
tions are  very  rapid  on  the  approach  of  a  thunder-storm. 
An  isolated  conductor  then  gives  out  such  quantities  of 
sparks  that  it  is  dangerous  to  approach  it,  as  was  fatally 
experienced  by  Professor  Richman,  at  Petersburg,  who 
was  struck  dead  by  a  globe  of  fire  from  the  extremity 
of  a  conductor,  while  making  experiments  on  atmos- 
pheric electricity.  There  is  no  instance  on  record  of  an 
electric  cloud  of  high  tension  being  dispelled  by  a  con- 
ducting rod  silently  withdrawing  the  electric  fluid ;  yet 
it  may  mitigate  the  stroke,  or  render  it  harmless  if  it 
should  come.  Copper  conductors  afford  the  best  pro- 
tection against  lightning,  especially  if  they  expose  a 
broad  surface,  since  the  electric  fluid  is  conveyed  along 
the  exterior  of  bodies.  Conductors  do  not  attract  the 
electric  fluid  from  the  clouds ;  their  object  is  to  carry 
it  off  in  case  of  a  stroke,  and  therefore  they  ought  to 
project  very  little,  if  at  all,  above  the  building. 

When  the  air  is  highly  rarefied  by  heat,  its  coercive 
power  is  diminished  so  that  the  electric  fluid  escapes 
from  the  clouds,  and  never  can  be  accumulated  beyond 


284  VELOCITY  OF  ELECTRICITY.       SECT.  XXVIII. 

a  certain  limit;  whence  those  lambent  diffuse  flashes  of 
lightning  without  thunder  so  frequent  in  warm  summer 
evenings." 

The  velocity  of  electricity  is  so  great,  that  the  most 
rapid  motion  which  can  be  produced  by  art  appears  to 
•  be  actual  rest  when  compared  with  it.  A  wheel  re- 
,  volving  with  celerity  sufficient  to  render  its  spokes  invis- 
\  ible,  when  illuminated  by  a  flash  of  lightning,  is  seen  for 
:  an  instant  with  all  its  spokes  distinct,  as  if  it  were  in  a 
state  of  absolute  repose ;  because,  however  rapid  the 
\  rotation  may  be,  the  light  has  come  and  already  ceased 
before  the  wheel  has  had  time  to  turn  through  a  sensible 
space.  This  beautiful  experiment  is  due  to  Professor 
Wheatstone,  as  well  as  the  following  variation  of  it, 
which  is  not  less  striking :  Since  a  sunbeam  consists  of 
a  mixture  of  blue,  yellow,  and  red  light,  if  a  circular 
piece  of  pasteboard  be  divided  into  three  sectors,  one  of 
which  is  painted  blue,  another  yellow,  and  a  third  red, 
it  will  appear  to  be  white  when  revolving  quickly,  be- 
cause of  the  rapidity  with  which  the  impressions  of  the 
colors  succeed  each  other  on  the  retina.  But  the  in- 
stant it  is  illuminated  by  an  electric  spark,  it  seems  to 
stand  still,  and  each  color  is  as  distinct  as  if  it  were  at 
rest.  This  transcendent  speed  of  the  electric  fluid  has 
been  ingeniously  measured  by  Professor  Wheatstone ; 
and  although  his  experiments  are  not  far  enough  ad- 
vanced to  enable  him  to  state  its  absolute  celerity,  he  has 
ascertained  that  it  much  surpasses  the  velocity  of  light. 
In  the  horizontal  diameter  of  a  small  disc  fixed  on  the 
wall  of  a  darkened  room  are  disposed  six  small  brass 
balls,  well  insulated  from  each  other.  An  insulated 
copper  wire  half  a  mile  long  is  disjoined  in  its  middle, 
and  also  near  its  two  extremities ;  the  six  ends  thus  ob- 
tained are  connected  with  the  six  balls  on  the  disc. 
When  an  electric  discharge  is  sent  through  the  wire  by 
connecting  its  two  extremities,  one  with  the  positive, 
and  the  other  with  the  negative  coating  of  a  Leyden 
jar,  three  sparks  are  seen  on  the  disc,  apparently  at  the 
same  instant.  At  the  distance  of  about  ten  feet,  a  small 
revolving  mirror  is  placed  so  as  to  reflect  these  three 
sparks  during  its  revolution.  From  the  extreme  velocity 
of  the  electricity,  it  is  clear,  that  if  the  three  sparks  bo 


SECT.  XXVIII.      VELOCITY  OF  ELECTRICITY.  285 

simultaneous,  they  will  be  reflected,  and  will  vanish  be- 
fore the  mirror  has  sensibly  changed  its  position,  how- 
ever rapid  its  rotation  may  be,  and  they  will  be  seen  in  a 
straight  line.  But  if  the  three  sparks  be  not  simultane- 
ously transmitted  to  the  disc — if  one,  for  example,  be  later 
than  the  other  two- — the  mirror  will  have  time  to  revolve 
through  an  indefinitely  small  arc  in  the  interval  between 
the  reflection  of  the  two  sparks  and  that  of  the  single 
one.  However,  the  only  indication  of  this  small  motion 
of  the  mirror  will  be,  that  the  single  spark  will  not  be 
reflected  in  the  same  straight  line  with  the  other  two, 
but  a  little  above  or  below  it,  for  the  reflection  of  all 
three  will  still  be, apparently  simultaneous,  the  time  in- 
tervening being  much  too  short  to  be  appreciated. 

Since  the  number  of  revolutions  which  the  revolving 
mirror  makes  in  a  second  are  known,  and  the  angular 
deviation  of  the  reflection  of  the  single  spark  from  the 
reflection  of  the  other  two  can  be  measured,  the  time 
elapsed  between  their  consecutive  reflections  can  be  as- 
certained. And  as  the  length  of  that  part  of  the  wire 
through  which  the  electricity  has  passed  is  given,  its  ve- 
locity may  be  found. 

Since  the  number  of  pulses  in  a  second  requisite  to 
produce  a  musical  note  of  any  pitch  is  known,  the  num- 
ber of  revolutions  accomplished  by  the  mirror  in  a  given 
time  may  be  determined  from  the  musical  note  produced 
by  a  tooth  or  peg  in  its  axis  of  rotation  striking  against  a 
card,  or  from  the  notes  of  a  siren  attached  to  the  axis. 
It  was  thus  that  Professor  Wheatstone  found  the  mir- 
ror which  he  employed  in  his  experiments  to  make  800 
revolutions  in  a  second;  and  as  the  angular  velocity  of 
the  reflected  image  in  a  revolving  mirror  is  double  that 
of  the  mirror  itself,  an  angular  deviation  of  one  degree 
in  the  appearance  of  the  two  sparks  would  indicate  an 
interval  of  the  576,000th  of  a  second ;  the  deviation  of 
half 'a  degree  would,  therefore,  indicate  more  than  the 
millionth  of  a  second.  The  use  of  sound  as  a  measure 
of  velocity  is  a  happy  illustration  of  the  connection  of  the 
physical  sciences. 

When  the  atmosphere  is  highly  charged  with  elec- 
tricity, it  not  unfrequentiy  happens  that  electric  light  in 
the  form  of  a  star  is  seen  on  the  topmast  and  yard-arms 


286  PHOSPHORESCENCE.  SECT.  XXVm. 

of  ships.  In  1831  the  French  officers  at  Algiers  were 
surprised  to  see  brushes  of  light  on  the  heads  of  their 
comrades,  and  at  the  points  of  their  fingers,  when  they 
held  up  their  hands.  This  phenomenon  was  well  known 
to  the  ancients,  who  reckoned  it  a  lucky  omen. 

Many  substances  in  decaying  emit  light,  which  is  at- 
tributed to  electricity,  such  as  fish  and  rotten  wood. 
Oyster  shells,  and  a  variety  of  minerals,  become  phos- 
phorescent at  certain  temperatures,  when  exposed  to 
electric  shocks  or  friction :  indeed  most  of  the  causes 
which  disturb  molecular  equilibrium  give  rise  to  phos- 
phoric phenomena.  The  minerals  possessing  this  prop- 
erty are  generally  colored  or  imperfectly  transparent ; 
and  though  the  color  of  this  light  varies  in  different  sub- 
stances, it  has  no  fixed  relation  to  the  color  of  the  min- 
eral. An  intense  heat  entirely  destroys  this  property, 
and  the  phosphorescent  light  developed  by  heat  has  no 
connection  with  light  produced  by  friction,  for  Sir  David 
Brewster  observed  that  bodies  deprived  of  the  faculty  of 
emitting  the  one  are  still  capable  of  giving  out  the  other. 
Among  the  bodies  which  generally  become  phosphores- 
cent when  exposed  to  heat,  there  are  some  specimens 
which  do  not  possess  this  property,  wherefore  phospho- 
rescence cannot  be  regarded  as  an  essential  character  of 
the  minerals  possessing  it.  Sulphuret  of  calcium,  known 
as  Canton's  phosphorus,  and  the  sulphuret  of  barium,  or 
Bologna  stone,  possess  the  phosphorescent  property  in 
an  eminent  degree,  and  M.  Edmond  Becquerel  has  shown 
that  on  these  substances  a  very  remarkable  phosphores- 
cent effect  is  produced  by  the  action  of  the  different 
rays  of  the  solar  spectrum.  In  former  times  Beccaria 
stated  that  the  violet  ray  was  the  most  energetic,  and 
the  red  ray  the  least  so,  in  exciting  phosphoric  light.  M. 
Becquerel  has  shown  that  two  luminous  bands  separated 
by  a  dark  one  are  excited  by  the  solar  spectrum  on  pa- 
per covered  with  a  solution  of  gum-arabic  and  strewed 
with  powdered  sulphuret  of  calcium.  One  of  the  lu- 
minous bands  occupies  the  space  under  the  least  refran- 
gible violet  rays,  and  the  other  that  beyond  the  lavender 
rays,  so  that  the  dark  band  lies  on  the  part  under  the 
extreme  violet  and  lavender  rays.  When  the  action  of 
the  spectral  light  is  continued,  the  whole  surface  beyond 


SJBCT.  XXVIII.  PHOSPHORESCENCE.  287 

the  least  refrangible  violet  shines,  the  luminous  bands 
already  mentioned  brightest,  but  all  the  space  from  the 
least  refrangible  violet  to  the  extreme  red  remains  dark. 
If  the  surface  prepared  with  either  the  sulphuret  of  cal- 
cium or  the  Bologna  stone  be  exposed  to  the  sun's  light 
for  a  short  time  it  becomes  luminous  all  over,  but  when 
in  this  state  a  solar  spectrum  is  thrown  upon  it,  the 
whole  remains  luminous  except  the  part  from  the  least 
refrangible  violet  to  the  extreme  red,  on  which  space 
the  light  is  extinguished ;  and  when  the  temperature  of 
this  surface  is  raised  by  a  lamp,  the  bright  parts  become 
more  luminous  and  the  dark  parts  remain  dark.  Glass 
stained  by  the  protoxide  of  copper,  which  transmits  only 
the  red  and  orange  rays  together  with  the  chemical  rays 
that  accompany  them,  has  ^he  same  effect  with  the  less 
refrangible  part  of  the  spectrum  ;  hence  there  can  be  no 
doubt  that  the  most  refrangible  and  obscure  rays  of  the 
spectrum  excite  phosphorescence,  while  all  the  less  re- 
frangible rays  of  light  and  heat  extinguish  it.  It  appears 
from  the  experiments  of  MM.  Biot  and  Becquerel  that 
electrical  disturbance  produces  these  phosphorescent 
effects.  There  is  thus  a  mysterious  connection  between 
the  most  refrangible  rays  and  electricity,  which  the  ex- 
periments of  iVI.  E.  Becquerel  confirm,  showing  that 
electricity  is  developed  during  chemical  action  by  the 
violet  rays,  that  it  is  very  feebly  developed  by  the  blue 
and  indigo,  but  that  none  is  excited  by  the  less  refrangi- 
ble part  of  the  spectrum. 

Paper  prepared  with  the  sulphuret  of  barium  when 
under  the  solar  spectrum  shows  only  one  space  of  max- 
imum luminous  intensity,  and  the  destroying  rays  are 
the  same  as  in  sulphuret  of  calcium. 

Thus  the  obscure  rays  beyond  the  extreme  violet 
possess  the  property  of  producing  light,  while  the  lumi- 
nous rays  have  the  power  of  extinguishing  it. 

The  phosphoric  spectrum  has  inactive  lines  which 
coincide  with  those  in  the  luminous  and  chemical  spec- 
tra at  least  as  far  as  it  extends,  but  in  order  to  be  seen, 
the  spectrum  must  be  received  for  a  few  seconds  upon 
the  prepared  surface  through,  an  aperture  in  a  dark 
room,  then  the  aperture  must  be  closed,  and  the  tem- 
perature of  the  surface  raised  two  or  three  hundred 


288  PHOSPHORESCENCE.  SECT.  XXVIII. 

degrees ;  the  phosphorescent  parts  then  shine  brilliantly, 
and  the  dark  lines  appear  black. 

Since  the  parts  of  similar  refrangibility  in  the  differ- 
ent spectra  are  traversed  by  the  same  dark  lines,  rays 
of  the  same  refrangibility  are  probably  absorbed  at  the 
same  time  by  the  different  media  through  which  they 
pass.  Multitudes  of  fish  are  endowed  with  the  power 
of  emitting  light  at  pleasure,  no  doubt  to  enable  them 
to  pursue  their  prey  at  depths  where  the  sunbeams  can- 
not penetrate.  Flashes  of  light  are  frequently  seen  to 
dart  along  a  shoal  of  herrings  or  pilchards  ;  and  the 
Medusa  tribes  are  noted  for  their  phosphorescent  brill- 
iancy, many  of  which  are  extremely  small,  and  so  nu- 
merous as  to  make  the  wake  of  a  vessel  look  like  a  stream 
of  silver.  Nevertheless,  the  luminous  appearance  which 
is  frequently  observed  in  the  sea  during  the  summer 
months  cannot  always  be  attributed  to  marine  animalcule, 
as  the  following  narrative  will  show : — 

Captain  Bonnycastle,  coming  up  the  Gulf  of  St.  Law- 
rence on  the  7th  of  September,  1826,  was  roused  by 
the  mate  of  the  vessel  in  great  alarm  from  an  unusual 
appearance.  It  was  a  starlight  night,  when  suddenly 
the  sky  became  overcast  in  the  direction  of  the  high 
land  of  Cornwallis  country,  and  an  instantaneous  and 
intensely  vivid  light,  resembling  the  aurora,  shot  out  of 
the  hitherto  gloomy  and  dark  sea  on  the  lee  bow,  which 
was  so  brilliant  that  it  lighted  everything  distinctly,  even 
to  the  mast-head.  The  light  spread  over  the  whole 
sea  between  the  two  shores,  and  the  waves,  which  be- 
fore had  been  tranquil,  now  began  to  be  agitated.  Cap- 
tain Bonnycastle  describes  the  scene  as  that  of  a  blazing 
sheet  of  awful  and  most  brilliant  light.  A  long  and  vivid 
line  of  light,  superior  in  brightness  to  ,the  parts  of  the 
sea  not  immediately  near  the  vessel,  showed  the  base 
of  the  high,  frowning,  and  dark  land  abreast :  the  sky 
became  lowering  and  more  intensely  obscure.  Long, 
tortuous  lines  of  light  showed  immense  numbers  of  very 
large  fish  darting  about  as  if  in  consternation.  The 
spritsail-yard  and  mizen-boom  were  lighted  by  the  glare, 
as  if  gas-lights  had  beenr  burning  directly  below  them ; 
and  until  just  before  dayoreak,  at  four  o'clock,  the  most 
minute  objects  were  distinctly  visible.  Day  broke  very 


SECT.  XXVIII.  AURORA  BOREALIS.  289 

slowly,  and  the  sun  rose  of  a  fiery  and  threatening  as- 
pect. Rain  followed.  Captain  Bonnycastle  caused  a 
bucket  of  this  fiery  water  to  be  drawn  up  ;  it  was  one 
mass  of  light  when  stirred  by  the  hand,  and  not  in  sparks 
as  usual,  but  in  actual  coruscations.  A  portion  of  the 
water  preserved  its  luminosity  for  seven  nights.  On 
the  third  night,  .the  scintillations  of  the  sea  reappeared  ; 
this  evening  the  sun  went  down  very  singularly,  exhibit- 
ing in  its  descent  a  double  sun  ;  and  when  only  a  few 
degrees  high,  its  spherical  figure  changed  into  that  of 
a  long  cylinder,  which  reached  the  horizon.  In  the 
night  the  sea  became  nearly  as  luminous  as  before,  but 
on  the  fifth  night  the  appearance  entirely  ceased.  Cap- 
tain Bonnycastle  does  not  think  it  proceeded  from  ani- 
malculae,  but  imagines  it  might  be  some  compound  of 
phosphorus,  suddenly  evolved  and  disposed  over  the  sur- 
face of  the  sea ;  perhaps  from  the  exuviae  or  secretions 
of  fish  connected  with  the  oceanic  salts,  muriate  of  soda, 

a-,nd  sulphate  of  magnesia. 

The  aurora  borealis  is  decidedly  an  electrical  phenom- 
enon, which  takes  place  in  the  highest  regions  of  the 
atmosphere,  since  it  is  visible  at  the  same  time  from 
places  very  far  distant  from  each  other.  It  is  somehow 
connected  with  the  magnetic  poles  of  the  earth,  and  oc- 
casions vibrations  in  the  magnetic  needle.  M.  Arago 
has  frequently  remarked  that  the  needle  was  powerfully 
agitated  at  Paris,  by  an  aurora  that  was  below  the  hori- 
zon, and  consequently  invisible,  but  whose  existence 
was  known  from  the  observations  of  the  polar  navigators. , 
The  aurora  has  never  been  seen  so  far  north  as  the  pole 
of  the  earth's  rotation,  nor  does  it  extend  to  low  latitudes. 
It  generally  appears  in  the  form  of  a  luminous  arch, 
stretching  more  or  less  from  east  to  west,  but  never  from 
north  to  south,  the  most  elevated  point  being  always  in 
the  magnetic  meridian  of  the  place  of  the  observer ;  and 
across  the  arch  the  coruscations  are  rapid,  vivid,  and  of 
various  colors,  but  whether  there  be  any  sound  is  still  a 
disputed  point.  A  similar  phenomenon  occurs  in  the  high 
latitudes  of  the  southern  hemisphere.  Dr.  Faraday- 
conjectures  that  the  electric  equilibrium  of  the  earth  is 
restored  by  the  aurora  conveying  the  electricity  from  the 
poles  to  the  equator. 

19  BB 


290  VOLTAIC  ELECTRICITY.  SECT.  XXIX. 


SECTION  XXIX. 

Voltaic  Electricity— The  Voltaic  Battery— Intensity— Quantity— Compari- 
son of  the  Electricity  of  Tension  with  Electricity  in  Motion— Luminous 
Effects — Decomposition  of  Water — Formation  of.  Crystals  by  Voltaic 
Electricity— Electrical  Fish. 

VOLTAIC  electricity  is  of  that  peculiar  kind  which  is 
elicited  by  the  force  of  chemical  action.  It  is  connected 
with  one  of  the  most  brilliant  periods  of  British  science, 
from  the  splendid  discoveries  to  which  it  led  Sir  Hum- 
phry Davy ;  and  it  has  acquired  additional  interest 
since  the  discovery  of  the  reciprocal  action  of  Voltaic 
and  magnetic  currents,  which  has  proved  that  magnetism 
is  only  an  effect  of  electricity,  and  that  it  has  no  existence 
as  a  distinct  or  separate  principle.  Consequently  Voltaic 
electricity,  as  immediately  connected  with  the  theory  of 
the  earth  and  planets,  forms  a  part  of  the  physical  ac- 
count of  their  nature. 

In  1790,  while  Galvani,  Professor  of  Anatomy  in  Bo- 
logna, was  making  experiments  on  electricity,  he  was 
surprised  to  see  convulsive  motions  in  the  limbs  of  a 
dead  frog  accidentally  lying  near  the  machine  during  an 
electrical  discharge.  Though  a  similar  action  had  been 
noticed  long  before  his  time,  he  was  so  much  struck  with 
this  singular  phenomenon,  that  he  examined  all  the  cir- 
cumstances carefully,  and  at  length  found  that  convulsions 
take  place  when  the  nerve  and  muscle  of  a  frog  are  con- 
nected by  a  metallic  conductor.  This  excited  the  atten- 
tion of  all  Europe  ;  and  it  was  not  long  before  Professor 
Volta  of  Pavia  showed  that  the  mere  contact  of  different 
bodies  is  sufficient  to  disturb  electrical  equilibrium,  and 
that  a  current  of  electricity  flows  in  one  direction  through 
a  circuit  of  three  conducting  substances.  From  this  he 
was  led,  by  acute  reasoning  and  experiment,  to  the  con- 
struction of  the  Voltaic  pile,  which,  in  its  early  form, 
consisted  of  alternate  discs  of  zinc  and  copper,  separated 
by  pieces  of  wet  cloth,  the  extremities  being  connected 
by  wires.  This  simple  apparatus,  perhaps  the  most 
wonderful  instrument  that  has  been  invented  by  the  in- 
genuity of  man,  by  divesting  electricity  of  its  sudden  and 


SECT.  XXIX.  THE  VOLTAIC  BATTERY.  291 

uncontrollable  violence,  and  giving  in  a  continued  stream 
a  greater  quantity  at  a  diminished  intensity,  has  exhibited 
that  fluid  under  a  new  and  manageable  form,  possessing 
powers  the  most  astonishing  and  unexpected.  As  the 
Voltaic  batteiy  has  become  one  of  the  most  important 
engines  of  physical  research,  some  account  of  its  present 
condition  may  not  be  out  of  place.) 

The  disturbance  of  electric  equilibrium,  and  a  devel- 
opment of  electricity,  invariably  accompany  the  chem- 
ical action  of  the  fluid  on  metallic  substances,  and  are 
most  plentiful  when  that  action  occasions  oxidation. 
Metals  vary  in  the  quantity  of  electricity  afforded  by 
their  combination  with  oxygen.  But  the  greatest 
abundance  is  developed  by  the  oxidation  of  zinc  by  weak 
sulphuric  acid.  [And  in  conformity  with  the  law  that 
one  kind  of  electricity  cannot  be  evolved  without  an 
equal  quantity  of  the  other  being  brought  into  activity, 
it  is  found  that  the  acid  is  positively,  and  the  zinc  nega- 
tively electric.  It  has  not  yet  been  ascertained  why 
equilibrium  is  not  restored  by  the  contact  of  these  two 
substances,  which  are  both  conductors,  and  in  opposite 
electrical  states.  However,  the  electrical  and  chemical 
changes  are  so  connected,  that  unless  equilibrium  be 
restored,  the  action  of  the  acid  will  go  on  languidly,  or 
stop  as  soon  as  a  certain  quantity  of  electricity  is  accu- 
mulated in  it.  Equilibrium  nevertheless  will  be  restored, 
and  the  action  of  the  acid  will  be  continuous,  if  a  plate  of 
copper  be  placed  in  contact  with  the  zinc,  both  being 
immersed  in  the  fluid ;  for  the  copper,  not  being  acted 
upon  by  the  acid,  will  serve  as  a  conductor  to  convey 
the  positive  electricity  from  the  acid  to  the  zinc,  and 
will  at  every  instant  restore  the  equilibrium,  and  then 
the  oxidation  of  the  zinc  will  go  on  rapidly.  (Thus 
three  substances  are  concerned  in  forming  a  voltaic 
circuit,  but  it  is  indispensable  that  one  of  them  should 
be  a  fluid,  j  The  electricity  so  obtained  will  be  very 
feeble  in  overcoming  resistances  offered  by  imperfect 
conductors  interposed  in  the  circuit,  or  by  very  long 
wires,  but  it  may  be  augmented  by  increasing  the  num- 
ber of  plates.  In  the  common  Voltaic  battery,  the 
electricity  which  the  fluid  has  acquired  from  the  first 
plate  of  zinc,  exposed  to  its  action,  is  taken  up  by  the 


292  THE  VOLTAIC  BATTERY.  SECT.  XXIX. 

copper  plate  belonging  to  the  second  pair,  and  transferred 
to  the  second  zinc  plate,  with  which  it  is  connected. 
The  second  plate  of  zinc  possessing  equal  powers,  and 
acting  in  conformity  with  the  first,  having  thus  acquired 
a  larger  portion  of  electricity  than  its  natural  share, 
communicates  a  larger  quantity  to  the  fluid  in  the  second 
cell.  This  increased  quantity  is  again  transferred  to 
the  next  pair  of  plates  ;  and  thus  every  succeeding  al- 
ternation is  productive  of  a  further  increase  in  the 
quantity  of  the  electricity  developed.  This  action, 
however,  would  stop  unless  a  vent  were  given  to  the 
accumulated  electricity,  by  establishing  a  communication 
between  the  positive  and  negative  poles  of  the  battery, 
by  means  of  wires  attached  to  the  extreme  plate  at  each 
end.  When  the  wires  are  brought  into  contact,  the 
Voltaic  circuit  is  completed,  the  electricities  meet  and 
neutralize  each  other,  producing  the  shock  and  other 
electrical  phenomena ;  and  then  the  electric  current 
continues  to  flow  uninterruptedly  in  the  circuit,  as  long 
as  the  chemical  action  lasts.  The  stream  of  positive 
electricity  flows  from  the  zinc  to  the  copper.  The 
construction  and  power  of  the  Voltaic  battery  has  been 
much  improved  of  late  years,  but  the  most  valuable 
recent  improvement  is  the  constant  battery  of  Professor 
Daniell.  In  all  batteries  of  the  ordinary  construction, 
the  power,  however  energetic  at  first,  rapidly  diminishes, 
and  ultimately  becomes  very  feeble.  Professor  Daniell 
found  that  this  diminution  of  power  is  occasioned  by  the 
adhesion  of  the  evolved  hydrogen  to  the  surface  of  the 
copper,  and  to  the  precipitation  of  the  sulphate  formed 
by  the  action  of  the  acid  on  the  zinc.  He  prevents  the 
latter  by  interposing  between  the  copper  and  the  zinc, 
in  the  cell  containing  the  liquid,  a  membrane  which, 
without  impeding  the  electric  current,  prevents  the 
transfer  of  the  salt;  and  the  former,  by  placing  between 
the  copper  and  the  membrane  solution  of  sulphate  of 
copper,  which  being  reduced  by  the  hydrogen  prevents 
the  adhesion  of  this  gas  to  the  metallic  surface.  Each 
element  of  the  battery  consists  of  a  hollow  cylinder  of 
copper,  in  the  axis  of  which  is  placed  a  cylindrical  rod  of 
zinc ;  between  the  zinc  and  the  copper  a  membranous 
bag  is  placed,  which  divides  the  cell  into  two  portions, 


SKCT.  XXIX.  THE  VOLTAIC  BATTERY.  293 

the  inner  of  which  is  filled  with  dilute  acid,  and  the  one 
nearer  the  copper  is  supplied  with  crystals  of  the  sul- 
phate of  that  metal.  The  battery  consists  of  several  of 
these  elementary  cells  connected  together  by  metallic 
wires,  the  zinc  rod  of  one  with  the  copper  cylinder  of 
that  next  to  it.  The  zinc  rods  are  amalgamated,  so  that 
local  action,  which  in  ordinaiy  cases  is  so  destructive  of 
the  zinc,  does  not  take  place,  and  no  chemical  action  is 
manifested  unless  the  circuit  be  completed.  The  rods 
are  easily  detached,  and  others  substituted  for  them 
when  worn  out.  This  battery,  which  possesses  con- 
siderable power,  and  is  constant  in  its  effects  for  a  very 
long  period  of  time,  is  greatly  superior  to  all  former  ar- 
rangements, either  as  an  instrument  of  research,  or  for 
exhibiting  the  ordinaiy  phenomena  of  Voltaic  electricity. 

A  battery  charged  with  water  alone,  instead  of  acid, 
is  very  constant  in  its  action,  but  the  quantity  of  elec- 
tricity it  developes  is  comparatively  very  small.  Mr. 
Cross  of  Broomfield  in  Somersetshire,  has  kept  a  bat- 
tery of  this  kind  in  full  force  during  twelve  months. 
M.  Becquerel  had  invented  an  instrument  for  comparing 
the  intensities  of  the  different  kinds  of  electricity  by 
means  of  weights,!  but  as  it  is  impossible  to  make  the 
comparison  with  Voltaic  electricity  produced  by  the  or- 
dinary batteries,  on  account  of  the  perpetual  variation 
to  which  the  intensity  of  the  current  is  liable,  he  has 
constructed  a  battery  which  affords  a  continued  stream 
of  electricity  of  uniform  power,  but  it  is  also  of  very 
feeble  force.  The  current  is  produced  by  the  chemical 
combination  of  an  acid  with  an  alkali. 

Metallic  contact  is  not  necessary  for  the  production  of 
Voltaic  electricity,  which  is  entirely  due  to  chemical 
action.  The  intensity  of  the  Voltaic  electricity  is  in 
proportion  to  the  intensity  of  the  affinities  concerned  in 
its  production,  and  the  quantity  produced  is  in  propor- 
tion to  the  quantity  of  matter  which  has  been  chem- 
ically active  during  its  evolution.  Dr.  Faraday  considers 
this  definite  production  to  be  one  of  the  strongest  proofs 
that  the  electricity  is  of  chemical  origin. 

Galvanic  or  Voltaic,  like  common  electricity,  may 
either  be  considered  to  consist  of  two  fluids  passing  in 
opposite  directions  through  the  circuit,  or,  if  the  hypoth- 

B  B2 


294  VOLTAIC  ELECTRICITY.  SECT.  XXIX. 

esis  of  one  fluid  be  adopted,  the  zinc  end  of  the  bat- 
tery may  be  supposed  to  have  an  excess  of  electricity, 
and  the  copper  end  a  deficiency.  Hence,  in  the  latter 
case,  the  zinc  is  the  positive  end  of  the  battery,  and  the 
copper  the  negative. 

Voltaic  electricity  is  distinguished  by  two  marked 
characters.  Its  intensity  increases  with  the  number  of 
plates — its  quantity  with  the  extent  of  their  surfaces. 
The  most  intense  concentration  of  force  is  displayed  by 
a  numerous  series  of  large  plates,  light  and  heat  are 
copiously  evolved,  and  chemical  decomposition  is  accom- 
plished with  extraordinary  energy ;  whereas  the  elec- 
tricity from  one  pair  of  plates,  whatever  their  size  may 
be,  is  so  feeble  that  it  gives  no  sign  either  of  attraction 
or  repulsion ;  and,  even  with  a  battery  consisting  of  a 
very  great  number  of  plates,  it  is  difficult  to  render  the 
mutual  attraction  of  its  two  wires  sensible,  though  of 
opposite  electricities. 

The  action  of  Voltaic  electricity  differs  in  some  re- 
spects materially  from  that  of  the  ordinary  kind.  When 
a  quantity  of  common  electricity  is  accumulated,  the 
restoration  of  equilibrium  is  attended  by  an  instantaneous 
violent  explosion,  accompanied  by  the  development  of 
light,  heat,  and  sound.  The  concentrated  power  of  the 
fluid  forces  its  way  through  every  obstacle,  disrupting 
and  destroying  the  cohesion  of  the  particles  of  the  bodies 
through  which  it  passes,  and  occasionally  increasing  its 
destructive  effects  by  the  conversion  of  fluids  into  steam 
from  the  intensity  of  the  momentary  heat,  as  when 
trees  are  torn  to  pieces  by  a  stroke  of  lightning.  Even 
the  vivid  light  which  marks  the  path  of  the  electric  fluid 
is  probably  owing  in  part  to  the  sudden  compression  of 
the  air  and  other  particles  of  matter  during  the  rapidity 
of  its  passage,  or  to  the  violent  and  abrupt  reunion  of 
the  two  fluids.  But  the  instant  equilibrium  is  restored 
by  this  energetic  action  the  whole  is  a-t  an  end.  On  the 
contrary,  when  an  accumulation  takes  place  in  a  Voltaic 
battery,  equilibrium  is  restored  the  moment  the  circuit 
is  completed.  But  so  far  is  the  electric  stream  from 
being  exhausted,  that  it  continues  to  flow  silently  and 
invisibly  in  an  uninterrupted  current  supplied  by  a  per- 
petual reproduction.  And  although  its  action  on  bodies 


S«CT.  XXIX.  VOLTAIC  ELECTRICITY.  295 

is  neither  so  sudden  nor  so  intense  as  that  of  common 
electricity,  yet  it  acquires  such  power  from  constant 
accumulation  and  continued  action,  that  it  ultimately 
surpasses  the  energy  of  the  other.  The  two  kinds  of 
electricity  differ  in  no  circumstance  more  than  in  the 
development  of  heat.  Instead  of  a  momentary  evolu- 
tion, which  seems  to  arise  from  a  forcible  compression 
of  the  particles  of  matter  during  the  passage  of  the  com- 
mon electric  fluid,  the  circulation  of  the  Voltaic  electricity 
is  accompanied  by  a  continued  development  of  heat, 
lasting  as  long  as  the  circuit  is  complete,  without  pro- 
ducing either  light  or  sound  ;  and  this  appears  to  be  its 
immediate  direct  effect,  independent  of  mechanical  ac- 
tion. Its  intensity  from  a  very  powerful  battery  is 
greater  than  that  of  any  heat  that  can  be  obtained  by 
artificial  means,  so  that  it  fuses  substances  which  resist 
the  action  of  the  most  powerful  furnaces.  The  temper- 
ature of  every  part  of  a  Voltaic  battery  itself  is  raised 
during  its  activity. 

When  the  battery  is  powerful,  the  luminous  effects  of 
Voltaic  electricity  are  very  brilliant.  But  considerable 
intensity  is  requisite  to  enable  the  electricity  to  force  its 
way  through  the  air  on  bringing  the  wires  "together 
from  the  opposite  poles.  Its  transit  is  accompanied  by 
light ;  and  in  consequence  of  the  continuous  supply  of 
the  fluid,  sparks  occur  every  time  the  contact  of  the 
wires  is  either  broken  or  renewed.  The  most  splendid 
artificial  light  known  is  produced  by  fixing  pencils  of 
charcoal  at  the  extremities  of  the  wires,  and  bringing 
them  into  contact.  This  light  is  the  more  remarkable, 
as  it  appears  to  be  independent  of  combustion,  since  the 
charcoal  suffers  no  change,  and  likewise  because  it  is 
equally  vivid  in  such  gases  as  do  not  contain  oxygen. 
Though  nearly  as  bright  as  solar  light,  it  differs  materi- 
ally from  it  when  analyzed  with  a  prism.  Professor 
Wheatstone  has  found  that  the  appearance  of  the  spec- 
trum of  the  Voltaic  spark  depends  upon  the  metal  from 
whence  the  spark  is  taken.  The  spectrum  of  that  from 
mercury  consists  of  seven  definite  rays,  separated  from 
each  other  by  dark  intervals ;  these  visible  rays  are  two 
orange  lines  close  together,  a  bright  green  line,  two 
bluish  green  lines  near  each  other,  a  very  bright  purple 


296  VOLTAIC  ELECTRICITY.  SECT.  XXIX. 

line,  and  lastly  a  violet  line.  The  spark  taken  from 
zinc,  cadmium,  tin,  bismuth,  and  lead  in  the  melted 
state,  gives  similar  results ;  but  the  number,  position, 
and  color  of  the  lines  vary  so  much  in  each  case,  and 
the  appearances  are  so  different,  that  the  metals  may  be 
easily  distinguished  from  each  other  by  this  mode  of 
investigation.  It  appears,  moreover,  that  the  light  does 
not  arise  from  the  combustion  of  the  metal ;  for  the 
Voltaic  spark  taken  from  mercury  successively  in  the 
vacuum  of  an  air-pump,  in  the  Torricellian  vacuum,  and 
in  carbonic  acid  gas,  is  precisely  the  same  as  when  the 
experiment  is  performed  in  the  air  or  in  oxygen  gas. 
Notwithstanding  the  difference  between  electric  and 
solar  light,  M.  Arago  is  inclined  to  attribute  the  intense 
light  and  heat  of  the  sun  to  electrical  action. 

Voltaic  electricity  is  a  powerful  agent  in  chemical 
analysis.  When  transmitted  through  conducting  fluids 
it  separates  them  into  their  constituent  parts,  which  it 
conveys  in  an  invisisible  state  through  a  considerable 
space  or  quantity  of  liquid  to  the  poles,  where  they 
come  into  evidence.  Numerous  instances  might  be 
given,  but  the  decomposition  of  water  is  perhaps  the 
most  simple  and  elegant.  Suppose  a  glass  tube  filled 
with  water  and  corked  at  both  ends  ;  if  one  of  the  wires 
of  an  active  Voltaic  battery  be  made  to  pass  through 
one  cork  and  the  other  through  the  other  cork,  into  the 
water,  so  that  the  extremities  of  the  two  wires  shall  be 
opposite  and  about  a  quarter  of  an  inch  asunder,  chemi- 
cal action  will  immediately  take  place,  and  gas  will  con- 
tinue to  rise  from  the  extremities  of  both  wires  till  the 
water  has  vanished.  If  an  electric  spark  j^e  then  sent 
through  the  tube,  the  water  will  reappear.  By  arrang- 
ing the  experiment  so  as  to  have  the  gas^iven  out  by 
each  wire  separately,  it  is  found  that  water  consists  of 
two  volumes  of  hydrogen  and  one  of  oxygen.  The  hy- 
drogen is  given  out  at  the  positive  wire  of  the  battery, 
and  the  oxygen  at  the  negative.  The  oxides  are  also 
decomposed  ;  the  oxygen  appears  at  the  positive  pole, 
and  the  metal  at  the  negative.  The  decomposition  of 
the  alkalies  and  earths  by  Sir  Humphry  Davy  formed 
a  remarkable  era  in  the  history  of  Science.  Soda, 
potass,  lime,  magnesia,  and  other  substances  heretofore 


S«CT.  XXIX.  FORMATION  OF  CRYSTALS.  297 

considered  to  be  simple  bodies  incapable  of  decomposi- 
tion, were  resolved  by  electric  agency  into  their  constit- 
uent parts,  and  proved  to  be  metallic  oxides,  by  that 
illustrious  philosopher.  /  All  chemical  changes  produced 
by  the  electric  fluid  arfcs  accomplished  on  the  same  prin- 
ciple ;  and  it  appears  that  in  general,  combustible  sub- 
stances, metals,  and  alkalies  go  to  the  negative  wire, 
while  acids  and  oxygen  are  evolved  at  the  positive. 
The  transfer  of  these  substances  to  the  poles  is  not  the 
least  wonderful  effect  of  the  Voltaic  battery.  Though 
the  poles  be  at  a  considerable  distance  from  one  another, 
nay,  even  in  separate  vessels,  if  a  communication  be 
only  established  by  a  quantity  of  wet  thread,  as  the  de- 
composition proceeds  the  component  parts  pass  through 
the  thread  in  an  invisible  state,  and  arrange  themselves 
at  their  respective  poles.  According  to  Dr.  Faraday, 
electro-chemical  decomposition  is  simply  a  case  of  the 
preponderance  of  one  set  of  chemical  affinities  more 
powerful  in  their  nature  over  another  set  which  are  less 
powerful.  The  great  efficacy  of  Voltaic  electricity  in 
chemical  decomposition  arises  from  the  continuance  of 
its  action ;  and  its  agency  appears  to  be  most  exerted 
on  fluids  and  substances  which,  by  conveying  the  elec- 
tricity partially  and  imperfectly,  impede  its  progress. 
But  it  is  now  proved  to  be  as  efficacious  in  the  compo- 
sition as  in  the  decomposition  or  analysis  of  bodies. 

It  had  been  observed  that  when  metallic  solutions  are 
subjected  to  galvanic  action,  a  deposition  of  metal,  some- 
times in  the  form  of  minute  crystals,  takes  place  on  the 
negative  wire.  By  extending  this  principle,  and  em- 
ploying a  very  feeble  Voltaic  action,  M.  Becquerel  has 
succeeded  in  forming  crystals  of  a  great  proportion  of 
the  mineral  substances,  precisely  similar  to  those  pro- 
duced by  nature.  The  electric  state  of  metallic  veins 
makes  it  possible  that  many  natural  crystals  may  have 
taken  their  form  from  the  action -of  electricity  bringing 
their  ultimate  particles,  when  in  solution,  within  the 
narrow  sphere  of  molecular  attraction  already  mentioned 
as  the  great  agent  in  the  formation  of  solids.  Both  light 
and  motion  favor  crystalization.  Crystals  which  form 
in  different  liquids  are  generally  more  abundant  on  the 
side  of  the  iar  exposed  to  the  light :  and  it  is  well  known 


298  ELCETROGILDING.  SECT.  XXIX. 

that  still  water,  cooled  below  32°,  starts  into  crystals  of 
ice  the  instant  it  is  agitated.  Light  and  motion  are 
intimately  connected  with  electricity,  which  may  there- 
fore have  some  influence  on  the  laws  of  aggregation; 
this  is  the  more  likely,  as  a  feeble  action  is  alone  neces- 
\  sary,  provided  it  be  continued  for  a  sufficient  time. 
Crystals  formed  rapidly  are  generally  imperfect  and 
soft,  and  M.  Becquerel  found  that  even  years  of  constant 
Voltaic  action  were  necessary  for  the  crystalization  of 
some  of  the  hard  substances.  If  this  law  be  general, 
how  many  ages  may  be  required  for  the  formation  of  a 
diamond  ? 

The  deposition  of  metal  from  a  metallic  solution  by 
galvanic  electricity  has  been  most  successfully  applied 
to  the  art  of  plating  and  gilding,  as  well  as  to  the  more 
delicate  process  of  copying  medals  and  copper  plates. 
Indeed,  not  metals  only,  but  any  object  of  art  or  nature 
may  be  coated  with  precipitated  metal,  provided  it  be 
first  covered  with  the  thinnest  film  of  plumbago,  which 
renders  a  non-conductor  sufficiently  conducting  to  re- 
ceive the  metal. 

Common  electricity,  on  account  of  its  high  tension, 
passes  through  water  and  other  liquids,  as  soon  as  it  is 
formed,  whatever  the  length  of  its  course  may  be.  Vol- 
taic electricity,  on  the  contrary,  is  weakened  by  the  dis- 
tance it  has  to  traverse.  Pure  water  is  a  very  bad  con- 
ductor ;  but  ice  absolutely  stops  a  current  of  Voltaic 
electricity  altogether,  whatever  be  the  power  of  the  bat- 
tery, although  common  electricity  has  sufficient  power 
to  overcome  its  resistance.  Dr.  Faraday  has  discovered 
that  this  property  is  not  peculiar  to  water ;  that,  with  a 
few  exceptions,  bodies  which  do  not  conduct  electricity 
when  solid,  acquire  that  property,  and  are  immediately 
decomposed,  when  they  become  fluid ;  and  in  general, 
that  decomposition  takes  place  as  soon  as  the  solution 
acquires  the  capacity  of  conduction,  which  has  led  him 
to  suspect  that  the  power  of  conduction  may  be  only  a 
consequence  of  decomposition. 

Heat  increases  the  conducting  power  of  some  sub- 
stances for  Voltaic  electricity,  and  of  the  gases  for  both 
kinds.  Dr.  Faraday  has  given  a  new  proof  of  the  con- 
nection between  heat  and  electricity,  by  showing  that 


Sscrr.  XXIX.  ELECTRICAL  FISH.  299 

in  general,  when  a  solid  which  is  not  a  metal  becomes 
fluid,  it  almost  entirely  loses  its  power  of  conducting 
heat,  while  it  acquires  a  capacity  for  conducting  elec- 
tricity in  a  high  degree. 

The  galvanic  fluid  affects  all  the  senses.  Nothing  can 
be  more  disagreeable  than  the  shock,  which  may  even 
be  fatal  if  the  battery  be  very  powerful.  A  bright  flash 
of  light  is  perceived  with  the  eyes  shut,  when  one  of 
the  wires  touches  the  face  and  the  other  the  hand.  By 
touching  the  ear  with  one  wire  and  holding  the  other, 
strange  noises  are  heard,  and  an  acid  taste  is  perceived 
when  the  positive  wire  is  applied  to  the  tip  of  the  tongue 
and  the  negative  wire  touches  some  other  part  of  it. 
By  reversing  the  poles  the  taste  becomes  alkaline.  It 
renders  the  pale  light  of  the  glow-worm  more  intense. 
Dead  animals  are  roused  by  it,  as  if  they  started  again 
into  life,  and  it  may  ultimately  prove  to  be  the  cause  of 
muscular  action  in  the  living. 

Several  fish  possess  the  faculty  of  producing  electrical 
effects.  The  most  remarkable  are  the  gymnotus  elec- 
tricus,  found  in  South  America ;  and  the  torpedo,  a 
species  of  ray,  frequent  in  the  Mediterranean.  The 
electrical  action  of  the  torpedo  depends  upon  an  appa- 
ratus apparently  analogous  to  the  Voltaic  pile,  which  the 
animal  has  the  power  of  charging  at  will,  consisting  of 
membranous  columns  filled  throughout  with  laminae,  sep- 
arated from  one  another  by  a  fluid.  The  absolute  quan- 
tity of  electricity  brought  into  circulation  by  the  torpedo 
is  so  great,  that  it  affects  the  decomposition  of  water, 
has  power  sufficient  to  make  magnets^  gives  very  severe 
shocks  and  the  electric  spark.  It  is  identical  in  kind 
with  that  of  the  galvanic  battery,  the  electricity  of  the 
under  surface  of  the  fish  being  the  same  with  the  neg- 
ative pole,  and  that  in  the  upper  surface  the  same  with 
the  positive  pole.  Its  manner  of  action  is,  however, 
somewhat  different ;  for  although  the  evolution  of  the 
electricity  is  continued  for  a  sensible  time,  it  is  inter- 
rupted, being  communicated  by  a  succession  of  dis- 
charges. 


300  TERRESTRIAL  MAGNETISM.  SECT.  XXX. 


SECTION  XXX.  „ 

Terrestrial  Magnetism — Magnetic  Poles — Lines  of  equal  and  no  Variation 
— The  Dip — The  Magnetic  Equator— Magnetic  Intensity — Secular,  peri- 
odic, and  transitory  Variations  in  the  Magnetic  Phenomena — Origin  of 
the  Mariner's  Compass— Natural  Magnets— Artificial  Magnets — Polarity 
— Induction — Intensity — Hypothesis  of  two  Magnetic  Fluids — Distribu- 
tion of  the  Magnetic  Fluid— Analogy  between  Magnetism  and  Electricity. 

IN  order  to  explain  the  other  methods  of  exciting 
electricity,  and  the  recent  discoveries  in  that  science,  it 
is  necessary  to  be  acquainted  with  the  general  theory 
of  magnetism,  and  also  with  the  magnetism  of  the  earth, 
the  director  of  the  mariner's  compass — his  guide  through 
the  ocean. 

The  distribution  of  terrestrial  magnetism  is  very  com- 
plicated, and  the  observations  simultaneously  made  at 
the  various  magnetic  establishments  recently  formed  in 
both  hemispheres  have  changed  many  of  the  opinions 
formerly  received  with  regard  to  that  science. 

Its  influence,  arising  from  unknown  causes  in  the  in- 
terior of  the  earth,  extends  over  every  part  of  its  surface, 
but  seems  to  be  independent  of  the  form  and  of  the 
peculiarities  of  the  exterior  of  our  planet  (a).  Its 
action  on  the  magnetic  needle  determines  the  magnetic 
poles  of  the  earth,  which  do  not  coincide  with  the  poles 
of  rotation. 

Mr.  Hansteen  of  Copenhagen  computed,  from  obser- 
vations in  various  parts  of  the  world,  that  there  are  two 
magnetic  poles  in  each  hemisphere,  while  M.  Gauss 
has  concluded  there  is  only  one  in  each  (A).  The 
position  of  one  of  these  poles  was  determined  by  our 
gallant  countrymen  when  endeavoring  to  accomplish  the 
north-west  passage  round  America.  It  is  situate  in  70° 
5'  17"  north  latitude,  and  96°  46'  45"  west  longitude. 
Another  northern  magnetic  pole  is  known  by  observa- 
tion to  be  in  Siberia,  somewhat  to  the  north  of  60°  north 
latitude  and  in  102°  east  longitude,  so  that  the  two  poles 
are  198°  46'  45"  asunder.  In  his  recent  voyage  to  the 
Antarctic  regions  Sir  James  Ross  ascertained  that  one 
of  the  southern  magnetic  poles  is  in  70°  south  latitude. 


SECT.  XXX.  THE  DIP.  301 

and  about  162°  east  longitude.     The  position  of  the 
other  south  magnetic  pole,  if  it  exists,  is  unknown. 

In  consequence  of  the  attraction  and  repulsion  of 
these  poles,  a  needle  suspended  so  as  to  move  freely  in 
a  horizontal  direction,  whether  it  be  magnetic  or  not, 
only  remains  in  equilibrio  when  in  the  magnetic  meridian, 
that  is,  when  it  is  .in  a  place  which  passes  through  a 
north  and  a  south  magnetic  pole.  In  some  places  the 
magnetic  meridian  coincides  with  the  terrestrial  me- 
ridian, and  m  these  a  magnetic  needle  freely  suspended, 
as  in  T;he  mariner's  'compass,  points  to  the  true  north ; 
but  if  it  be  carried  successively  to  different  places  on 
the  earth's  surface  its  direction  will  deviate,  sometimes 
to  the  east,  and  sometimes  to  the  west  of  the  true  north. 
Imaginary  lines  drawn  on  the  globe  through  all  the 
places  where  the  needle  points  due  north  and  south  are 
called  lines  of  no  variation.  Imaginary  lines  drawn 
through  all  those  places  whore  the  needle  deviates  from 
the  geographical  meridian  by  an  equal  quantity,  are  lines 
of  equal  variation. 

A  magnetic  needle  suspended  so  as  to  be  movable 
only  in  a  vertical  plane  dips,  or  becomes  more  and  more 
inclined  to  the  horizon  the  nearer  it  is  brought  to  a 
magnetic  pole,  and  there  it  becomes  vertical.  Lines 
of  equal  dip  are  such  as  may  be  imagined  to  pass 
through  all  those  points  on  the  globe  where  the  dipping 
needle  makes  the  same  angle  with  the  horizon.  In 
some  places  the  dipping  needle  becomes  horizontal,  and 
there  the  influences  of  the  north  and  south  poles  are 
balanced,  and  an  imaginary  line  passing  through  all  such 
places  is  the  magnetic  equator.  In  going  north  from 
the  magnetic  equator  one  end  of  the  dipping  needle  dips 
more  and  more  till  it  becomes  perpendicular  at  the 
north  magnetic  pole,  while  in  proceeding  south  from 
the  magnetic  equator  the  other  end  of  the  dipping 
needle  dips,  and  at  last  becomes  perpendicular  at  the 
south  magnetic  pole.  The  magnetic  equator  does  not 
coincide  with  the  terrestrial  equator :  it  appears  to  be 
an  irregular  curve  passing  round  the  earth,  inclined 
to  the  earth's  equator  at  an  angle  of  about  12°,  and 
crossing  it  in  several  points,  the  position  of  which  seems 
stiU  to  be  uncertain.  According  to  some  accounts,  three 
Cc 


302  INTENSITY  OF  MAGNETIC  FORCE.    SECT.  XXX. 

points  have  been  ascertained  in  which  that  curve  cuts 
the  equator;  yet  Captain  Duperry,  who  crossed  it  re- 
peatedly, affirms,  from  his  own  observations  combined 
with  those  of  M.  Jules  de  Bosville  and  of  Colonel 
Sabine,  that  it  crosses  the  terrestrial  equator  in  two 
points  only,  and  those  diametrically  opposite  one  to  the 
other,  and  not  far  from  the  meridian  of  Paris.  One  of 
these  nodes  he  places  in  the  Atlantic,  the  other  in  the 
Pacific  ocean.  He  finds  that  the  magnetic  equator 
deviates  but  little  from  the  terrestrial  equator  in  that 
part  of  the  Pacific  where  there  are  only  a  few  scattered 
islands  (6),  that  as  the  islands  become  more  frequent 
the  deviation  increases,  and  arrives  at  a  maximum  both 
to  the  north  and  south  in  traversing  the  African  and 
American  continents ;  and  that  the  symmetry  of  the 
northern  and  southern  segments  of  this  curve  is  much 
greater  than  was  imagined. 

The  intensity  of  the  magnetic  force  is  different  in  dif- 
ferent parts  of  the  earth.  If  a  magnetic  needle,  freely 
suspended  so  as  to  move  horizontally,  and  at  rest  in  a 
magnetic  meridian,  be  drawn  any  number  of  degrees 
from  that  position,  it  will  make  a  certain  number  of  os- 
cillations before  it  resumes  its  state  of  rest.  The  inten- 
sity of  the  magnetic  force  is  determined  from  these  os- 
cillations, in  the  same  manner  that  the  intensity  of  the 
gravitating  and  electrical  forces  is  known  from  the  vibra- 
tions of  the  pendulum  and  the  balance  of  torsion  (c) : 
and  in  all  these  cases  it  is  proportional  to  the  squares  of 
the  number  of  oscillations  performed  in  a  given  time, 
consequently  a  comparison  of  the  number  of  vibrations 
accomplished  by  the  same  needle  during  the  same  time 
in  different  parts  of  the  earth's  surface  will  determine 
the  variations  in  the  magnetic  action.  By  this  method 
it  was  discovered  that  the  intensity  of  the  magnetic  force 
increases  from  the  equator  toward  the  poles ;  but  the 
foci  of  the  greatest  total  intensity  of  the  magnetic  force 
seem  neither  to  coincide  with  the  magnetic  nor  rotatory 
poles  of  the  earth  (d).  One  of  these  foci,  according  to 
Colonel  Sabine's  magnetic  chart,  is  situate  about  the  47° 
south  latitude  and  140°  east  longitude,  while  another  of 
less  energy  is  in  60°  south  latitude  and  235°  east  longi- 
tude. The  point  of  least  total  magnetic  intensity  on  the 


SICT.  XXX.  DISTURBANCES.  303 

whole  globe  is  by  the  same  chart  about  the  25°  south 
latitude  and  12°  west  longitude.  In  the  northern  hem- 
isphere the  foci  of  maximum  intensity  are  in  lat.  54°  32' 
N.,  long.  261°  27'  E.,  and  lat.  71°  20'  N.,  long.  119°  57'  E., 
according  to  M.  Gauss's  calculations.  The  magnetic 
intensity  appears  to  be  doubled  in  the  ascent  from  the 
equator  to  Baffin's  bay. 

Such  are  the  principal  phenomena  of  terrestrial  mag- 
netism, but  it  is  subject  to  secular,  periodical,  and  tran- 
sient disturbances  still  imperfectly  known.  In  the  north- 
ern hemisphere,  the  poles,  the  lines  of  equal  and  no 
variation,  the  equator,  and  in  short  the  whole  system  is 
gradually  moving  toward  the  east,  so  that  the  relations 
observed  in  Europe  two  centuries  ago  have  now  reached 
the  limits  between  Europe  and  Asia,  while  other  parts 
of  the  system  have  moved  gradually  over  to  us  from  the 
west.  In  the  southern  hemisphere  the  secular  motion 
of  the  poles  and  of  the  whole  system  is  in  a  contrary 
direction.  The  cause  of  these  secular  disturbances  is 
altogether  unknown. 

The  horizontal  needle  or  compass  at  any  one  place  is 
also  subject  to  periodic  and  transient  perturbations. 
Great  disturbances  occur  on  the  same  day,  or  nearly  on 
the  same  day,  in  different  years,  from  causes  unknown. 

There  are  also  disturbances  which,  according  to  the 
observations  of  M.  Kreil,  in  Milan,  depend  on  the  decli- 
nation of  the  moon  and  her  distance  from  the  earth ; 
others  of  shorter  duration  seem  to  be  intimately  con- 
nected with  the  motion  of  the  sun  in  regard  to  the  mag- 
netic meridian  of  the  place  of  observation.  In  conse- 
quence of  the  latter,  the  needle  in  the  same  place  is 
subject  to  diurnal  variations:  in  our  latitudes  the  end 
that  points  to  the  north  moves  slowly  westward  during 
the  forenoon,  and  returns  to  its  mean  position  about  ten 
hi  the  evening;  it  then  deviates  to  the  eastward  and 
again  returns  to  its  mean  position  about  ten  in  the 
morning. 

M.  Kupffer  of  Casan  ascertained  that  there  is  a  noctur- 
nal as  well  as  a  diurnal  variation,  depending  in  his  opinion 
upon  a  variation  in  the  magnetic  equator.  Magnetic 
storms,  or  sudden  and  great  but  transient  disturbances, 
take  place  occasionally  in  the  compass,  which  are  per- 


304  CHANGES  OF  MAGNETIC  INTENSITY.  SECT.  XXX. 

ceived  simultaneously  over  widely  extended  regions; 
while  others  of  less  magnitude  and  duration  occur  more 
frequently,  and  are,  equally  witty  the  greater,  not  amena- 
ble to  any  known  laws. 

The  dip  is  subject  to  a  secular  variation,  and  according 
to  Colonel  Sabine  has  been  decreasing  in  northern  lati- 
tudes for  the  last  fifty  years  at  the  rate  of  three  minutes 
annually,  and  is  probably  owing  to  the  secular  motion  of 
the  magnetic  equator.  There  are  disturbances  also  in 
the  dip  of  a  periodic  nature,  and  others  very  transient, 
which  M.  Kreil  attributes  to  weak  shocks  of  earth- 
quakes, having  observed  that  the  greatest  vertical  dis- 
turbances have  almost  always  coincided  with  consider- 
able earthquakes  even  when  they  occurred  in  remote 
regions. 

The  magnetic  intensity  is  subject  to  various  changes. 
M.  Hansteen  has  found  that  it  has  been  decreasing  an- 
nually at  Christiana,  London,  and  Paris  at  the  rate  of 
its  235th,  725th,  and  1020th  parts  respectively,  which 
he  attributes  to  the  motion  of  the  Siberian  magnetic 
pole.  The  moon  increases  the  onagnetic  intensity  in 
our  hemisphere  :  but  her  influence  differs  with  her  dif- 
ference of  position  in  the  heavens.  The  times  of  vibra- 
tion of  the  needle  are  less  when  the  moon  has  south 
declination  than  when  she  has  north,  and  they  are  less 
when  she  is  in  perigee  than  in  apogee.  It  is  still  doubtful 
whether  magnetic  intensity  varies  with  the  height  above 
the  earth  or  not. 

The  diurnal  variation  in  the  horizontal  intensity  ob- 
served by  M.  Hansteen  at  Christiana  is  probably  owing 
to  the  sun's  influence  :  indeed  the  whole  of  the  magnetic 
disturbances  have  been  ascribed  to  that  cause ;  and  he 
has  even  found  a  general  resemblance  between  the  iso- 
thermal lines  and  the  lines  of  equal  dip  on  the  surface 
of  the  earth :  yet  in  the  present  state  of  our  knowledge 
the  magnetic  phenomena  can  only  be  regarded  as  the 
effects  of  a  combination  of  causes  whose  separate  action 
is  still  unknown. 

The  inventor  of  the  mariner's  compass,  like  most  of 
the  early  benefactors  of  mankind,  is  unknown.  It  is 
even  doubted  which  nation  first  made  use  of  magnetic 
polarity  to  determine  positions  on  the  surface  of  the  globe. 


SKCT.  XXX.  THE  MARINER'S  COMPASS.  305 

But  it  is  said  that  a  rude  form  of  the  compass  was  in- 
vented in  Upper  Asia,  and  conveyed  thence  by  the 
Tartars  to  China,  where  the  Jesuit  missionaries  found 
traces  of  this  instrument  having  been  employed  as  a 
guide  to  land  travelers  in  very  remote  antiquity.  From 
that  the  compass  spread  over  the  East,  and  was  imported 
into  Europe  by  the  Crusaders,  and  its  construction  im- 
proved by  an  artist  of  Amalfi,  on  the  coast  of  Calabria. 
It  seems  that  the  Chinese  only  employed  twenty-four 
cardinal  divisions,  which  the  Germans  increased  to 
thirty-two,  and  gave  the  points  the  names  which  they 
still  bear. 

The  variation  of  the  compass  was  'unknown  until  Co- 
lumbus, during  his  first  voyage,  observed  that  the  needle 
declined  from  t^ie  meridian  as  he  advanced  across  the 
Atlantic.  The  dip  of  the.  magnetic  needle  was  first  no- 
ticed by  Robert  Norman,  in  the  year  1576. 

Very  delicate  experiments  have  shown  that  all  bodies 
are  more  or  less  susceptible  of  magnetism.  Many  of 
the  gems  give  signs  of  it ;  cobalt  and  nickel  always  pos- 
sess the  properties  of  attraction  and  repulsion.  But  the 
magnetic  agency  is  most  powerfully  developed  in  iron, 
and  in  that  particular  ore  of  iron  called  the  loadstone, 
which  consists  of  the  protoxide  and  the  peroxide  of  iron, 
together  with  small  portions  of  silica  and  alumina.  A 
metal  is  often  susceptible  of  magnetism  if  it  only  contains 
the  130,000th  part  of  its  weight  of  iron,  a  quantity  too 
small  to  be  detected  by  any  chemical  test. 

The  bodies  in  question  are  naturally  magnetic,  but 
that  property  may  be  imparted  by  a  variety  of  methods, 
as  by  friction  with  magnetic  bodies,  or  juxtaposition  to 
them ;  but  none  is  more  simple  than  percussion.  A  bar 
of  hard  steel,  held  in  the  direction  of  the  dip,  will  be- 
come a  magnet  on  receiving  a  few  smart  blows  with  a 
hammer  on  its  upper  extremity ;  and  M.  Hansteen  has 
ascertained  that  every  substance  has  magnetic  poles 
when  held  in  that  position,  whatever  the  materials  may 
be  of  which  it  is  composed. 

One  of  the  most  distinguishing  marks  of  magnetism  is 

polarity,  or  the  property  a  magnet  possesses,  when  freely 

suspended,  of  spontaneously  pointing  nearly  north  and 

south,  and  always  returning  to  that  position  wiien  dis- 

20  c  c  2 


306  POLARITY  AND  INDUCTION.  SECT.  XXX. 

turbed.  Another  property  of  a  magnet  is  the  attraction 
of  uninagnetized  iron.  Both  poles  of  a  magnet  attract 
iron,  which  in  return  attracts  either  pole  of  the  magnet 
with  an  equal  and  contrary  force.  The  magnetic  in- 
tensity is  most  powerful  at  the  poles,  as  may  easily  be 
seen  by  dipping  the  magnet  into  iron  filings,  which  will 
adhere  abundantly  to  each  pole,  while  scarcely  any 
attach  themselves  to  the  intermediate  parts.  The 
action  of  the  magnet  on  unmagnetized  iron  is  confined 
to  attraction,  whereas  the  reciprocal  agency  of  magnets 
is  characterized  by  a  repulsive  as  well  as  an  attractive 
force,  for  a  north  pole  repels.a  north  pole,  and  a  south 
repels  a  south  pole.  But  a  north  and  a  south  pole 
mutually  attract  one  another,  which  proves  that  there 
are  two  distinct  kinds  of  magnetic  forces,  directly  op- 
posite in  their  effects,  though  similar  in  their  mode  of 
action. 

Induction  is  the  power  which  a  magnet  possesses  of 
exciting  temporary  or  permanent  magnetism  in  such 
bodies  in  its  vicinity  as  are  capable  of  receiving  it.  By 
this  property  the  mere  approach  of  a  magnet  renders 
iron  or  steel  magnetic,  the  more  powerfully  the  less  the 
distance.  When  the  north  pole  of  a  magnet  is  brought 
near  to,  and  in  the  line  with,  an  unmagnetized  iron  bar, 
the  bar  acquires  all  the  properties  of  a  perfect  magnet; 
the  end  next  the  north  pole  of  the  magnet  becomes  a 
south  pole,  while  the  remote  end  becomes  a  north  pole. 
Exactly  the  reverse  takes  place  when  the  south  pole  is 
presented  to  the  bar ;  so  that  each  pole  of  a  magnet 
induces  the  opposite  polarity  in  the  adjacent  end  of  the 
bar,  and  the  same  polarity  in  the  remote  extremity ; 
consequently  the  nearest  extremity  of  the  bar  is  at- 
tracted, and  the  farther  repelled ;  but  as  the  action  is 
greater  on  the  adjacent  than  on  the  distant  part,  the 
resulting  force  is  that  of  attraction.  By  induction,  the 
iron  bar  not  only  acquires  polarity,  but  the  power  of 
inducing  magnetism  in  a  third  body ;  and  although  all 
these  properties  vanish  from  the  iron  as  soon  as  the 
magnet  is  removed,  a  lasting  increase  of  intensity  is 
generally  imparted  to  the  magnet  itself  by  the  reaction 
of  the  temporary  magnetism  of  the  iron.  -Iron  acquires 
magnetism  more  rapidly  than  steel,  yet  it  loses  it  us 


S«cr.  XXX.  EDUCTION  OF  MAGNETISM.  307 

quickly  on  the  removal  of  the  magnet,  whereas  the 
steel  is  impressed  with  a  lasting  polarity. 

A  certain  time  is  requisite  for  the  induction  of  mag- 
netism, and  it  may  be  accelerated  by  anything  that 
excites  a  vibratory  motion  in  the  particles  of  the  steel, 
such  as  the  smart  stroke  of  the  hammer,  or  heat  suc- 
ceeded by  sudden  cold.  A  steel  bar  may  be  converted 
into  a  magnet  by  the  transmission  of  an  electric  discharge 
through  it;  and  as  its  efficacy  is  the  same  in  whatever 
direction  the  electricity  passes,  the  magnetism  arises 
from  its  mechanical  operation  exciting  a  vibration  among 
the  particles  of  steel.  It  has  been  observed  that  the 
particles  of  iron  easily  resume  their  neutral  state  after 
induction,  but  that  those  of  steel  resist  the  restoration 
of  magnetic  equilibrium,  or  a  return  to  the  neutral  state  ; 
it  is  therefore  evident,  that  any  cause  which  removes 
or  diminishes  the  resistance  of  the  particles  will  tend  to 
destroy  the  magnetism  of  the  steel ;  consequently,  the 
same  mechanical  means  which  develop  magnetism  will 
also  destroy  it.  On  that  account  a  steel  bar  may  lose 
its  magnetism  by  any  mechanical  concussion,  such  as  by 
falling  on  a  hard  substance,  a  blow  with  a  hammer,  and 
heating  to  redness,  which  reduces  the  steel  to  a  state  of 
softness.  The  circumstances  which  determine  whether 
it  shall  gain  or  lose,  are  its  position  with  respect  to  the 
magnetic  equator,  and  the  higher  or  lower  intensity  of 
its  previous  magnetic  state. 

Polarity  of  one  kind  only  cannot  exist  in  any  portion 
of  iron  or  steel ;  in  whatever  manner  the  intensities  of 
the  two  kinds  of  polarity  may  be  diffused  through  a  mag- 
net, they  exactly  balance  or  compensate  one  another. 
The  northern  polarity  is  confined  to  one-half  of  a  mag- 
net, and  the  southern  to  the  other,  and  they  are  gener- 
ally concentrated  in  or  near  the  extremities  of  the  bar. 
When  a  magnet  is  broken  across  its  middle,  each  frag- 
ment is  at  once  converted  into  a  perfect  magnet ;  the 
part  which  originally  had  a  north  pole  acquires  a  south 
pole  at  the  fractured  end  ;  the  part  that  originally  had  a 
south  pole  gets  a  north  pole  ;  and  as  far  as  mechanical 
division  can  be  carried,  it  is  found  that  each  fragment, 
however  small,  is  a  perfect  magnet. 

A  comparison  of  the  number  of  vibrations  accomplished 


308  LAW  OF  MAGNETIC  INTENSITY.        SECT.  XXX. 

by  the  same  needle,  during  the  same  time,  at  different 
distances  from  a  magnet,  gives  the  law  of  magnetic  in- 
tensity, which  follows  the  inverse  ratio  of  the  squares  of 
the  distances, — a  law  that  is  not  affected  by  the  inter- 
vention of  any  substance  whatever  between  the  magnet 
and  the  needle,  provided  that  substance  be  not  itself 
susceptible  of  magnetism.  Induction  and  the  reciprocal 
action  of  magnets  are  therefore  subject  to  the  laws  of 
mechanics ;  but  the  composition  and  resolution  of  the 
forces  are  complicated,  in  consequence  of  four  forces 
being  constantly  in  activity,  two  in  each  magnet. 

Mr.  Were  Fox,  who  has  paid  much  attention  to  this 
branch  of  the  science,  has  lately  discovered  that  the  law 
of  the  magnetic  force  changes  from  the  inverse  squares 
of  the  distances,  to  the  simple  inverse  ratio,  when  the 
distance  between  two  magnets  is  as  small  as  from  the 
fourth  to  the  eighth  of  an  inch,  or  even  as  much  as  half 
an  inch  when  the  magnets  are  large.  He  found,  that 
in  the  case  of  repulsion,  the  change  takes  place  at  a  still 
greater  distance,  especially  when  the  two  magnets  differ 
materially  in  intensity. 

There  can  hardly  be  a  doubt  but  that  all  the  phenom- 
ena of  magnetism,  like  those  of  electricity,  may  be  ex- 
plained on  the  hypothesis  of  one  ethereal  fluid,  which  is 
condensed  or  redundant  in  the  positive  pole,  and  deficient 
in  the  negative  ;  a  theory  that  accords  best  with  the  sim- 
plicity and  general  nature  of  the  laws  of  creation  ;  never- 
theless, Baron  Poisson  has  adopted  the  hypothesis  of 
two  extremely  rare  fluids  pervading  all  the  particles  of 
iron,  and  incapable  of  leaving  them.  Whether  the  par- 
ticles of  these  fluids  are  coincident  with  the  molecules 
of  the  iron,  or  that  they  only  fill  the  interstices  between 
them,  is  unknown  and  immaterial.  But  it  is  certain  that 
the  sum  of  all  the  magnetic  molecules,  added  to  the  sum 
of  all  the  spaces  between  them,  whether  occupied  by 
matter  or  not,  must  be  equal  to  the  whole  volume  of  the 
magnetic  body.  When  the  two  fluids  in  question  are 
combined  they  are  inert,  so  that  the  substances  contain- 
ing them  show  no  signs  of  magnetism ;  but  when  sepa- 
rate they  are  active,  the  molecules  of  each  of  the  fluids 
attracting  those  of  the  opposite  kind,  and  repelling  those 
of  the  same  kind.  The  decomposition  of  the  united 


SECT.  XXX.        BARON  POISSON'S  HYPOTHESIS.  309 

fluids  is  accomplished  by  the  inductive  influence  of  either 
of  the  separate  fluids ;  that  is  to  say,  a  ferruginous  body 
acquires  polarity  by  the  approach  of  either  the  south  or 
north  pole  of  the  magnet.  The  magnetic  fluids  pervade 
each  molecule  of  the  mass  of  bodies,  and  in  all  proba- 
bility the  electric  fluid  does  the  same,  though  it  appears 
to  be  confined  to  the  surface  ;  if  so,  a  compensation  must 
take  place  among  the  internal  forces.  The  electric 
fluid  has  a  perpetual  tendency  to  escape,  and  does  es- 
cape, when  not  prevented  by  the  coercive  power  of  the 
surrounding  air  and  other  non-conducting  bodies.  Such 
a  tendency  does  not  exist  in  the  magnetic  fluids,  which 
never  quit  the  substance  that  contains  them  under  any 
circumstances  whatever ;  nor  is  any  sensible  quantity  of 
either  kind  of  polarity  ever  transferred  from  one  part  to 
another  of  the  same  piece  of  steel.  It  appears  that  the 
two  magnetic  fluids,  when  decomposed  by  the  influence 
of  magnetizing  forces,  only  undergo  a  displacement  to 
an  insensible  degree  within  the  body.  The  action  of  all 
the  particles  so  displaced  upon  a  particle  of  the  magnetic 
fluid  in  any  particular  situation,  compose  a  resultant 
force,  the  intensity  and  direction  of  which  it  is  the  prov- 
ince of  the  analyst  to  determine.  In  this  manner  M. 
Poisson  has  proved  that  the  result  of  the  action  of  all 
the  magnetic  elements  of  a  magnetized  body,  is  a  force 
equivalent  to  the  action  of  a  very  thin  stratum  covering 
the  whole  surface  of  a  body,  and  consisting  of  the  two 
fluids — the  austral  and  the  boreal,  occupying  different 
parts  of  it ;  in  other  words,  the  attractions  and  repul- 
sions externally  exerted  by  a  magnet,  are  exactly  the 
same  as  if  they  proceeded  from  a  very  thin  stratum  of 
each  fluid  occupying  the  surface  only,  both  fluids  being 
in  equal  quantities,  and  so  distributed  that  their  total 
action  upon  all  the  points  in  the  interior  of  the  body  is 
equal  to  nothing.  Since  the  resulting  force  is  the  differ- 
ence of  the  two  polarities,  its  intensity  must  be  greatly 
inferior  to  that  of  either. 

In  addition  to  the  forces  already  mentioned,  there 
must  be  some  coercive  force  analogous  to  friction,  which 
arrests  the  particles  of  both  fluids,  so  as  first  to  oppose 
their  separation,  and  then  to  prevent  their  reunion.  In 
soft  iron  the  coercive  force  is  either  wanting  or  ex- 


310  ANALOGY  OF  MAGNETISM  SECT.  XXX. 

tremely  feeble,  since  the  iron  is  easily  rendered  mag- 
netic by  induction,  and  as  easily  loses  its  magnetism  ; 
whereas  in  steel  the  coercive  force  is  extremely  ener- 
getic, because  it  prevents  the  steel  from  acquiring  the 
magnetic  properties  rapidly,  and  entirely  hinders  it 
from  losing  them  when  acquired.  The  feebleness  of 
the  coercive  force  in  iron,  and  its  energy  in  steel,  with 
regard  to  the  magnetic  fluids,  is  perfectly  analogous  to 
the  facility  of  transmission  afforded  to  the  electric  fluid 
by  non-electrics,  and  the  resistance  it  experiences  in 
electrics.  At  every  step  the  analogy  between  magnet- 
ism and  electricity  becomes  more  striking.  The  agency 
of  attraction  and  repulsion  is  common  to  both;  the  pos- 
itive and  negative  electricities  are  similar  to  the  northern 
and  southern  polarities,  and  are  governed  by  the  same 
laws,  namely,  that  between  like  powers  there  is  repul- 
sion, and  between  unlike  powers  there  is  attraction. 
Each  of  these  four  forces  is  capable  of  acting  most  ener- 
getically when  alone  ;  but  as  the  electric  equilibrium  is 
restored  by  the  union  of  the  two  electric  states,  and 
magnetic  neutrality  by  the  combination  of  the  two  polar- 
ities, they  respectively  neutralize  each  other  when 
joined.  All  these  forces  vary  inversely  as  the  squares 
of  the  distances,  and  consequently  come  under  the  same 
mechanical  laws.  A  like  analogy  extends  to  magnetic 
and  electrical  induction.  Iron  and  steel  are  in  a  state  of 
equilibrium  when  the  two'magnetic  polarities  conceived 
to  reside  in  them  are  equally  diffused  throughout  the 
whole  mass,  so  that  they  are  altogether  neutral.  But 
this  equilibrium  is  immediately  disturbed  on  the  approach 
of  the  pole  of  a  magnet,  which  by  induction  transfers 
one  kind  of  polarity  to  one  end  of  the  iron  or  steel  bar, 
and  the  opposite  kind  to  the  other — effects  exactly  simi- 
lar to  electrical  induction.  There  is  even  a  correspond- 
ence between  the  fracture  of  a  magnet  and  that  of  an 
electric  conductor ;  for  if  an  oblong  conductor  be  elec- 
trified by  induction,  its  two  extremities  will  have  opposite 
electricities ;  and  if  in  that  state  it  be  divided  across  the 
middle,  the  two  portions,  when  removed  to  a  distance 
from  one  another,  will  each  retain  the  electricity  that 
has  been  induced  upon  it.  The  analogy,  however,  does 
not  extend  to  transference.  A  body  may  transfer  a  re- 


SECT.  XXX.  AND  ELECTRICITY.  311 

dundant  quantity  of  positive  electricity  to  another,  or 
deprive  another  of  its  electricity,  the  one  gaining  at  the 
expense  of  the  other ;  but  there  is  no  instance  of  a  body 
possessing  only  one  kind  of  polarity.  With  this  excep- 
tion, there  is  such  perfect  correspondence  between  the 
theories  of  magnetic  attractions  and  repulsions  and  elec- 
tric forces  in  conducting  bodies,  that  they  not  only  are 
the  same  in  principle,  but  are  determined  by  the  same 
formulae.  Experiment  concurs  with  theory  in  proving 
the  identity  of  these  two  unseen  influences.  Hence  if 
the  electrical  phenomena  be  due  to  a  modification  of  the 
ethereal  medium,  the  magnetic  phenomena  must  be 
owing  to  an  analogous  cause,  and  therefore,  notwithstand- 
ing the  high  authority  of  M.  Poisson,  they  must  also  be 
attributed  to  the  redundancy  and  defect  of  only  one  fluid. 

With  reference  to  the  subject  of  this  chapter  I  have 
received  the  following  information  from  Colonel  Sabine, 
one  of  the  best  authorities  in  this  branch  of  science. 

The  passage  marked  (A)  confounds  under  the  com- 
mon term  of  "  magnetic  pole,"  two  things  which  are 
alike  distinct  in  conception  and  different  in  reality. 
These  are,  1st — the  localities  on  the  globe  where  the 
needle  is  vertical,  or  the  horizontal  force  0 ;  and  2d — 
the  localities  where  the  magnetic  forces  acting  on  the 
surface  of  the  globe  have  a  maximum  intensity,  around 
which  the  isodynamic  lines  on  the  surface  arrange  them- 
selves in  curves,  and  in  departing  from  which  in  every 
direction  (on  the  surface)  the  intensity  of  the  force  is 
found  to  decrease. 

The  progress  of  terrestrial  magnetism  has  been  greatly 
impeded  by  mistakes  arising  from  the  different  under- 
standings which  different  people  have  of  what  is  meant 
by  the  term  magnetic  pole.  It  is  the  more  important 
to  have  clear  ideas  and  a  correct  knowledge  of  facts  in 
this  matter,  because  the  facts  of  science  are  not  such  as 
in  any  respect  to  justify  a  confusion  of  terms ;  not  one 
of  the  localities  where  the  intensity  of  the  force  is  a 
maximum  coincides  with  a  position  where  the  dip  is 
90°  ;  nor  does  a  dip  of  90°  anywhere  coincide  with  a 
position  where  the  force  is  a  maximum. 

There  is  in  each  hemisphere  one  locality  where  the 


312  TWO  MAGNETIC  POLES.  SECT.  XXX. 

dip  is  90°,  and  two  localities  where  the  force  forms  a 
center  of  greatest  intensity  around  which  the  isodynamic 
lines  arrange  themselves.  The  localities  of  dip  90°  are 
rather  spaces  than  points :  they  are  the  major  axes  of 
small  ovals  on  the  surface  of  the  sphere ;  consequently 
they  are  linear  rather  than  circular  spaces.  The  spot 
where  Captain  Ross  observed  the  needle  so  nearly  ver- 
tical in  1831  marks  the  approximate  position  of  that  lo- 
cality at  that  epoch.  This  position  is,  as  Mrs.  Som- 
erville  states,  about  70°  north,  and  97°  west.  The 
isodynamic  centers  in  the  same  hemisphere  are  situ- 
ated, one  in  America,  the  other  in  Siberia.  The  ob- 
servations made  anterior  to  1837,  which  are  collected 
and  arranged  in  Colonel  Sabine's  report  to  the  British 
Association  of  that  year,  gave,  when  treated  by  M. 
Gauss  according  to  the  formation  of  the  "Allgemeine 
Theorie,"  the  American  maximum  in  55°  north  and  97° 
west,  and  the  Siberian  in  71°  north  and  116°  east.  The 
more  recent  observations  of  Messrs.  Lefroy  and  I>ocke, 
who  have  traveled  in  America  expressly  for  the  more 
accurate  determination  of  what  appears  so  important  a 
datum  in  terrestrial  physics,  and  whose  results  are  at 
this  moment  being  arranged  on  a  chart  on  which  Colonel 
Sabine  is  about  to  trace  the  lines  of  highest  intensity  in 
America,  show  that  the  center  of  those  curves  is  yet 
farther  to  the  southward  by  some  degrees  (consequently 
still  more  removed  from  the  position  where  the  dip  is 
90°)  than  was  supposed  in  1837. 

The  two  maxima  of  force  are  not  of  equal  strength : 
the  Siberian  is  somewhat  the  weaker  of  the  two.  The 
positions  of  both  undergo  secular  change,  and  both  in 
the  same  direction,  viz.  to  the  eastward.  The  secular 
change  of  the  weaker  or  Siberian  maximum  is  far  more 
considerable  than  that  of  the  other.  The  secular 
changes  of  the  isoclinal  and  isogonic  curves  correspond 
with  those  of  the  two  systems  of  forces  indicated  by 
distinct  maxima  having  unequal  movements  of  transla- 
tion. The  higher  isoclinal  curves  are  oval,  having  their 
major  axes  in  the  line  of  direction  joining  the  two  points 
of  maximum  intensity.  The  general  arrangement  in  the 
south  hemisphere  is  strictly  analogous :  but  the  two 
centers  of  force  are  at  this  epoch  separated  by  a  less  in- 


SICT.  XXX.  THE  MAGNETIC  ATLAS.  313 

terval  of  longitude  than  in  the  north  hemisphere.  Their 
respective  longitudes,  derived  from  the  observations  of 
the  antarctic  expedition  which  Colonel  Sabine  has  re- 
duced and  published  in  the  Phil.  Trans.,  are  approxi- 
mately 130°  and  220°  east.  The  latitudes  are  not  de- 
rivable from  the  observations  with  equal  approximation  ; 
but  they  do  not  appear  to  differ  much  from  the  corres- 
ponding latitudes  in  the  north ;  i.  e.  the  stronger  about 
50°  or  55°  south,  and  the  weaker  about  70°  south.  Here 
also  the  weaker  maximum  has  a  very  considerable  sec- 
ular movement,  amounting,  as  Colonel  Sabine  has  given 
reason  to  believe  in  the  Phil.  Trans,  of  last  year,  to 
nearly  50°  of  longitude  in  250  years  :  the  secular  change 
in  the  southern  hemisphere  being  to  the  westward, 
while  that  in  the  northern  is  to  the  eastward. 

The  dip  of  90°  is  far  removed  from  either  of  these 
localities ;  its  approximate  position  may  be  called  about 
73°  south  and  147°  east;  but  the  isoclinal  curve  of  89° 
will  doubtless  be  more  correctly  given  when  the  Pagoda 
returns  from  the  completion  of  the  survey,  and  when 
the  whole  of  the  observations  in  the  southern  hemis- 
phere are  combined  and  treated  according  to  the  formulae 
of  the  *•  Allgemeine  Theorie." 

The  object  of  the  geographical  branch  of  the  magnetic 
observations  of  the  last  few  years  has  been  to  obtain 
determinations,  with  the  improved  instruments  of  the 
present  time,  in  every  accessible  part  of  the  globe,  with 
a  view  of  combining  the  results  into  magnetic  charts  of 
the  three  elements  drawn  directly  from  the  observations, 
and  corresponding  to  the  present  epoch.  The  Magnetic 
Atlas  will  then  be  recomputed  by  the  methods  described 
in  Gauss' "  Allgemeine  Theorie."  The  observation  part 
is  nearly  accomplished. 

(a)  This  is  by  no  means  established  ;  the  distribution 
of  land  and  water  appears  to  have  considerable  influence 
on  the  form  of  the  magnetic  equator,  as  Mrs.  Somer- 
ville  states  at  (6). 

(c)  In  the  balance  of  torsion,  the  intensity  of  electrical 
forces  is  not  measured  by  oscillations,  but  by  the  torsiojj 
necessary  to  destroy  the  deviation  produced* 

(d)  Refer  to  note  (4). 

Dn 


314  ELECTRO-MAGNETISM.  SECT.  XXXI. 


SECTION  XXXI. 

Discovery  of  Electro-Magnetism — Deflection  of  the  Magnetic  Needle  by  a 
Current  of  Electricity — Direction  of  the  Force — Rotatory  Motion  by  Elec- 
tricity— Rotation  of  a  Wire  and  a  Magnet— Rotation  of  a  Magnet  about 
its  Axis— Of  Mercury  and  Water — Electro- Magnetic  Cylinder  or  Helix — 
Suspension  of  a  Needle  in  a  Helix — Electro-Magnetic  Induction — Tem- 
porary Magnets — The  Galvanometer. 

THE  disturbing  effects  of  the  aurora  borealis  and  light- 
.ning  on  the  mariner's  compass  had  been  long  known. 
In  the  year  1819,  M.  Oersted,  Professor  of  Natural 
Philosophy  at  Copenhagen,  discovered  that  a  current  of 
Voltaic  electricity  exerts  a  powerful  influence  on  a  mag- 
netized needle.  This  observation  has  given  rise  to  the 
theory  of  electro-magnetism — the  most  interesting  sci- 
ence of  modern  times,  whether  it  be  considered  as  lead- 
ing us  a  step  farther  in  generalization,  by  identifying 
two  agencies  hitherto  referred  to  different  causes,  or  as 
developing  a  new  force,  unparalleled  in  the  system  of 
the  world,  which,  overcoming  the  retardation  from  fric- 
tion, and  the  obstacle  of  a  resisting  medium,  maintains 
a  perpetual  motion,  often  vainly  attempted,  but  appa- 
rently impossible  to  be  accomplished  by  means  of  any 
other  force  or  combination  of  forces  than  the  one  in 
question. 

When  the  two  poles  of  a  Voltaic  battery  are  connect- 
ed by  a  metallic  wire,  so  as  to  complete  a  circuit,  the 
electricity  flows  without  ceasing.  If  a  straight  portion 
of  that  wire  be  placed  parallel  to,  and  horizontally  above, 
a  magnetized  needle  at  rest  in  the  magnetic  meridian, 
but  freely  poised  like  the  mariner's  compass,  the  action 
of  the  electric  current  flowing  through  the  wire  will 
instantly  cause  the  needle  to  change  its  position.  Its 
extremity  will  deviate  from  the  north  toward  the  east 
or  west,  according  to  the  direction  in  which  the  current 
is  flowing ;  and  on  reversing  the  direction  of  the  current, 
the  motion  of  the  needle  will  be  reversed  also.  The 
numerous  experiments  that  have  been  made  on  the 
magnetic  and  electric  fluids,  as  well  as  those  on  the  vari- 
ous relative  motions  of  a  magnetic  needle  under  the 
influence  of  galvanic  electricity,  arising  from  all  possible 


S«cr.  XXXf.   DEFLECTION  OP  THE  NEEDLE.         315 

positions  of  the  conducting  wire,  and  every  direction  of 
the  Voltaic  current,  together  with  all  the  other  phe- 
nomena of  electro-magnetism,  are  explained  by  Dr. 
Roget  in  some  excellent  articles  on  these  subjects  in  the 
Library  of  Useful  Knowledge. 

All  the  experiments  tend  to  prove  that  the  force 
emanating  from  the  electric  current,  which  produces 
such  effects  on  the  magnetic  needle,  acts  at  right  angles 
to  the  current,  and  is  therefore  unlike  any  force  hith- 
erto known.  The  action  of  all  the  forces  in  nature  is 
directed  in  straight  lines,  as  far  as  we  know ;  for  the 
curves  described  by  the  heavenly  bodies  result  from  the 
composition  of  two  forces ;  whereas  that  which  is  ex- 
erted by  an  electrical  current  upon  either  pole  of  a 
magnetic  has  no  tendency  to  cause  the  pole  to  approach 
or  recede,  but  to  rotate  about  it.  If  the  stream  of  elec- 
tricity be  supposed  to  pass  through  the  center  of  a  circle 
whose  plane  is  perpendicular  to  the  current,  the  di- 
rection of  the  force  exerted  by  the  electricity  will  always 
be  in  the  tangent  to  the  circle,  or  at  right  angles  to  its 
radius  (N.  217).  Consequently  the  tangential  force  of 
the  electricity  has  a  tendency  to  make  the  pole  of  a 
magnet  move  in  a  circle  round  the  wire  of  the  battery. 
Mr.  Barlow  has  proved  that  the  action  of  each  particle 
of  the  electric  fluid  in  the  wire,  on  each  particle  of  the 
magnetic  fluid  in  the  needle,  varies  inversely  as  the 
squares  of  the  distances. 

Rotatory  motion  was  suggested  by  Dr.  Wollaston. 
Dr.  Faraday  was  the  first  who  actually  succeeded  in 
making  the  pole  of  a  magnet  rotate  about  a  vertical 
conducting  wire.  In  order  to  limit  the  action  of  the 
electricity  to  one  pole,  about  two-thirds  of  a  small  mag- 
net were  immersed  in  mercury,  the  lower  end  being 
fastened  by  a  thread  to  the  bottom  of  the  vessel  con- 
taining the  mercury.  When  the  magnet  was  thus  floating 
almost  vertically  with  its  north  pole  above  the  surface,  a 
current  of  positive  electricity  was  made  to  descend  per- 
pendicularly through  a  wire  touching  the  mercury,  and 
immediately  the  magnet  began  to  rotate  from  left  to 
right  about  the  wire.  The  force  being  uniform,  the 
rotation  was  accelerated  till  the  tangential  force  was 
balanced  by  the  resistance  of  the  mercury,  when  it  be- 


316  ROTATION  BY  ELECTRICITY.        SECT.  XXXI. 

came  constant.  Under  the  same  circumstances  the 
south  pole  of  the  magnet  rotates  from  right  to  left.  It 
is  evident  from  this  experiment,  that  the  wire  may  also 
be  made  to  perform  a  rotation  round  the  magnet,  since 
the  action  of  the  current  of  electricity  on  the  pole  of  the 
magnet  must  necessarily  be  accompanied  by  a  corres- 
ponding reaction  of  the  pole  of  the  magnet  on  the  elec- 
tricity in  the  wire.  This  experiment  has  been  accom- 
plished by  a  vast  number  of  contrivances,  and  even  a 
small  battery,  consisting  of  two  plates,  has  performed 
the  rotation.  Dr.  Faraday  produced  both  motions  at 
the  same  time  in  a  vessel  containing  mercury  ;  the  wire 
and  the  magnet  revolved  in  one  direction  about  a  com- 
mon center  of  motion,  each  following  the  other. 

The  next  step  was  to  make  a  magnet,  and  also  a  cyl- 
inder, revolve  about  their  own  axes,  which  they  do  with 
great  rapidity.  Mercury  has  been  made  to  rotate  by 
means  of  Voltaic  electricity,  and  Professor  Ritchie  has 
exhibited  in  the  Royal  Institution  the  singular  spectacle 
of  the  rotation  of  water  by  the  same  means,  while  the 
vessel  containing  it  remained  stationary.  The  water 
was  in  a  hollow  double  cylinder  of  glass,  and  on  being 
made  the  conductor  of  electricity,  was  observed  to  re- 
volve in  a  regular  vortex,  changing  its  direction  as  the 
poles  of  the  battery  were  alternately  reversed.  Pro- 
fessor Ritchie  found  that  all  the  diiferent  conductors 
hitherto  tried  by  him,  such  as  water,  charcoal,  &c.,  give 
the  same  electro-magnetic  results  when  transmitting  the 
same  quantity  of  electricity,  and  that  they  deflect  the 
magnetic  needle  in  an  equal  degree,  when  their  res- 
pective axes  of  conduction  are  at  the  same  distance  from 
it.  But  one  of  the  most  extraordinary  effects  of  the 
new  force  is  exhibited  by  coiling  a  copper  wire,  so  as  to 
form  a  helix  or  corkscrew,  and  connecting  the  extremi- 
ties of  the  wires  with  the  poles  of  a  galvanic  battery. 
If  a  magnetized  steel  bar  or  needle  be  placed  within  the 
screw,  so  as  to  rest  upon  the  lower  part,  the  instant  a 
current  of  electricity  is  sent  through  the  wire  of  the 
helix,  the  steel  bar  starts  up  by  the  influence  of  this  in- 
visible power,  and  remains  suspended  in  the  air  in  op- 
position to  the  force  of  gravitation  (N.  218).  The  effect 
of  the  electro-magnetic  power  exerted  by  each  turn  of 


XXXI.     ELECTRO-MAGNETIC  INDUCTION  317 

the  wire  is  to  urge  the  north  pole  of  the  magnet  in  one 
direction,  and  the  south  pole  in  the  other.  The  force 
thus  exerted  is  multiplied  in  degree  and  increased  in  ex- 
tent by  each  repetition  of  the  turns  of  the  wire,  and  in 
consequence  of  these  opposing  forces  the  bar  remains 
suspended.  This  helix  has  all  the  properties  of  a  mag- 
net while  the  electrical  current  is  flowing  through  it, 
and  may  be  substituted  for  one  in  almost  every  experi- 
ment. It  acts  as  if  it  had  a  north  pole  at  one  extremity 
and  a  south  pole  at  the  other,  and  is  attracted  and  re- 
pelled by  the  poles  of  a  magnet  exactly  as  if  it  were  one 
itself.  All  these  results  depend  upon  the  course  of  the 
electricity  ;  that  is,  on  the  direction  of  the  turns  of  the 
screw,  according  as  it  is  from  right  to  left,  or  from  left 
to  right,  being  contrary  in  the  two  cases. 

The  action  of  Voltaic  electricity  on  a  magnet  is  not 
only  precisely  the  same  with  the  action  of  two  magnets 
on  one  another,  but  its  influence  in  producing  temporary 
magnetism  in  iron  and  steel  is  also  the  same  with  mag- 
netic induction.  The  term  induction,  when  appb'ed  to 
electric  currents,  expresses  the  power  which  these 
currents  possess  of  inducing  any  particular  state  upon 
matter  in  their  immediate  neighborhood,  otherwise  neu- 
tral or  indifferent.  For  example,  the  connecting  wire 
of  a  galvanic  battery  holds  iron  filings  suspended  like  an 
artificial  magnet,  as  long  as  the  current  continues  to 
flow  through  it ;  and  the  most  powerful  temporary  mag- 
nets that  have  ever  been  made  are  obtained  by  bending 
a  thick  cylinder  of  soft  iron  into  the  form  of  a  horse- 
shoe, and  surrounding  it  with  a  coil  of  thick  copper  wire 
covered  with  silk,  to  prevent  communication  between 
its  parts.  When  this  wire  forms  part  of  a  galvanic  cir- 
cuit, the  iron  becomes  so  highly  magnetic,  that  a  tem- 
porary magnet  of  this  kind,  made  by  Professor  Henry, 
of  the  Albany  Academy,  in  the  United  States,  sustained 
nearly  a  ton  weight.  The  iron  loses  its  magnetic  power 
the  instant  the  electricity  ceases  to  circulate,  and  ac- 
quires it  again  as  instantaneously  when  the  circuit  is  re- 
newed. Temporary  magnets  have  been  made  by  Pro- 
fessor Moll  of  Utrecht,  upon  the  same  principle,  capable 
of  supporting  200  pounds'  weight,  by  means  of  a  battery 
of  one  plate  less  than  half  an  inch  square,  consisting  of 

DD2 


318  ELECTRO-MAGNETIC  INDUCTION.     SKCT.  XXXI. 

two  metals  soldered  together.  It  is  truly  wonderful 
that  an  agent,  evolved  by  so  small  an  instrument,  and 
diffused  through  a  large  mass  of  iron,  should  communi- 
cate a  force  which  seems  so  disproportionate.  Steel 
needles  are  rendered  permanently  magnetic  by  electrical 
induction ;  the  effect  is  produced  in  a  moment,  and  as 
readily  by  juxtaposition  as  by  contact ;  the  nature  of 
the  poles  depends  upon  the  direction  of  the  current, 
and  the  intensity  is  proportional  to  the  quantity  of  elec- 
tricity. 

•It  appears  that  the  principle  and  characteristic  phe- 
nomena of  the  electro-magnetic  science  are,  the  evolu- 
tion of  a  tangential  and  rotatory  force  exerted  between 
a  conducting  body  and  a  magnet ;  and  the  transverse 
induction  of  magnetism  by  the  conducting  body  in  such 
.substances  as  are  susceptible  of  it. 

The  action  of  an  electric  current  causes  a  deviation  of 
the  compass  from  the  plane  of  the  magnetic  meridian. 
In  proportion  as  the  needle  recedes  from  the  meridian, 
the  intensity  of  the  force  of  terrestrial  magnetism  in- 
creases, while  at  the  same  time  the  electro-magnetic 
force  diminishes ;  the  number  of  degrees  at  which  the 
needle  stops,  showing  where  the  equilibrium  between 
these  two  forces  takes  place,  will  indicate  the  intensity 
of  the  galvanic  current.  The  galvanometer,  constructed 
upon  this  principle,  is  employed  to  measure  the  inten- 
sity of  galvanic  currents  collected  and  conveyed  to  it  by 
wires.  This  instrument  is  rendered  much  more  sensi- 
ble by  neutralizing  the  effects  of  the  earth's  magnetism 
on  the  needle,  which  is  accomplished  by  placing  a  sec- 
ond magnetized  needle  so  as  to  counteract  the  action  of 
the  earth  on  the  first — a  precaution  requisite  in  all  del- 
icate magnetica}  experiments. 

'Electro-magnetic  induction  has  been  elegantly  and 
usefully  employed  by  Professor  Wheatstone  as  a  mov- 
ing power  in  a  telegraph,  by  which  intelligence  is  con- 
veyed in  a  time  quite  inappreciable,  since  the  electricity 
would  make  the  circuit  of  the  globe  in  the  tenth  of  a 
second. 


S«cr.  XXXII.  ELECTRO-DYNAMICS.  319 


SECTION  XXXII. 

Electro- Dynamics — Reciprocal  Action  of  Electric  Currents — Identity  of 
Electro-Dynamic  Cylinders  and  Magnets — Differences  between  the  Ac- 
tion of  Voltaic  Electricity  and  Electricity  of  Tension— Effects  of  a  Voltaic 
Current — Ampere's  Theory. 

THE  science  of  electro-magnetism,  which  must  ren- 
der the  name  of  M.  Oersted  ever  memorable,  relates  to 
the  reciprocal  action  of  electrical  and  magnetic  currents : 
M.  Ampere,  by  discovering  the  mutual  action  of  elec- 
trical currents  on  one  another,  has  added  a  new  branch 
to  the  subject,  to  which  he  has  given  the  name  of  elec- 
tro-dynamics. 

When  electric  currents  are  passing  through  two  con- 
ducting wires,  so  suspended  or  supported  as  to  be  capa- 
ble of  moving  both  toward  ?.nd  from  one  another,  they 
show  mutual  attraction  or  repulsion,  according  as  the 
currents  are  flowing  in  the  same  or  in  contrary  direc- 
tions ;  the  phenomena  varying  with  the  relative  inclina- 
tions and  positions  of  the  streams  of  electricity.  The 
mutual  action  of  such  currents,  whether  they  flow  in  the 
same  or  in  contrary  directions,  whether  they  be  parallel, 
perpendicular,  diverging,  converging,  circular,  or  heliacal, 
all  produce  different  kinds  of  motion  in  a  conducting 
wire,  both  rectilineal  and  circular,  and  also  the  rotation 
of  a  wire  helix,  such  as  that  described,  now  called  aii 
electro-dynamic  cylinder,  on  account  of  some  improve- 
ments in  its  construction  (N.  219).  And  as  the  hypoth- 
esis of  a  force  varying  inversely  as  the  squares  of  the 
distances  accords  perfectly  with  all  the  observed  phe- 
nomena, these  motions  come  under  the  same  laws  of 
dynamics  and  analysis  as  any  other  branch  of  physics. 

Electro-dynamic  cylinders  act  on  each  other  precisely 
as  if  they  were  magnets  during  the  time  the  electricity 
is  flowing  through  them.  All  the  experiments  that  can 
be  performed  with  the  cylinder  might  be  accomplished 
with  a  magnet.  That  end  of  the  cylinder  in  which  the 
current  of  positive  electricity  is  moving  hi  a  direction 
similar  to  the  motion  of  the  hands  of  a  watch,  acts  as  the 
south  pole  of  a  magnet,  and  the  other  end,  in  which  the 


320  ACTION  OF  ELECTRIC  CURRENTS.    SECT.  XXXH. 

current  is  flowing  in  a  contrary  direction,  exhibits  north- 
ern polarity. 

The  phenomena  mark  a  very  decided  difference  be- 
tween the  action  of  electricity  in  motion  or  at  rest,  that 
is,  between  Voltaic  and  common  electricity ;  the  laws 
they  follow  are  in  many  respects  of  an  entirely  different- 
nature,  though  the  electricities  themselves  are  identical. 
Since  Voltaic  electricity  flows  perpetually,  it  cannot  be 
accumulated,  and  consequently  has  no  tension,  or  ten- 
dency to  escape  from  the  wires  which  conduct  it.  Nor 
do  these  wires  either  attract  or  repel  light  bodies  -in 
their  vicinity,  whereas  ordinary  electricity  can  be  accu- 
mulated in  insulated  bodies  to  a  great  degree,  and  in 
that  state  of  rest  the  tendency  to  escape  is  proportional 
to  the  quantity  accumulated  and  the  resistance  it  meets 
with.  In  ordinary  electricity,  the  law  of  action  is  that 
dissimilar  electricities  attract,  and  similar  electricities 
repel  one  another.  ,  In  Voltaic  electricity,  on  the  con- 
^trary,  similar  currents,  or  such  as  are  moving  in  the 
same  direction,  attract  one  another,  while  a  mutual  re- 
pulsion is  exerted  between  dissimilar  currents,  or  such 
as  flow  in  opposite  directions.  Common  electricity 
escapes  when  the  pressure  of  the  atmosphere  is  re- 
moved, but  the  electro-dynamical  effects  are  the  same 
whether  the  conductors  be  in  air  or  in  vacuo. 

The  effects  produced  by  a  current  of  electricity  de- 
pend upon  the  celerity  of  its  motion  through  a  conduct- 
ing wire.  Yet  we  are  ignorant  whether  the  motion  be 
uniform  or  varied,  but  the  method  of  transmission  has  a 
marked  influence  on  the  results  ;  for  when  it  flows  with- 
out intermission,  it  occasions  a  deviation  in  the  magnetic 
needle,  but  it  has  no  effect  whatever  when  its  motion  is 
discontinuous  or  interrupted,  like  the  current  produced 
by  the  common  electrical  machine  when  a  communica- 
tion is  made  between  the  positive  and  negative  con- 
ductors. 

M.  Ampere  has  established  a  theoiy  of  electro-mag- 
netism suggested  by  the  analogy  between  electro-dy- 
namic cylinders  and  magnets,  founded  upon  the  recip- 
rocal attraction  of  electric  currents,  to  which  all  the  phe- 
nomena of  magnetism  and  electro-magnetism  may  be 
reduced,  by  assuming  that  the  magnetic  properties 


BKCT.  XXXII.    ACTION  OF  ELECTRIC  CURRENTS.  321 

which  bodies  possess  derive  these  properties  from  cur- 
rents of  electricity  circulating  about  every  part  in  one 
uniform  direction.  Although  every  particle  of  a  magnet 
possesses  like  properties  with  the  whole,  yet  the  general 
effect  is  the  same  as  if  the  magnetic  properties  were 
confined  to  the  surface.  Consequently  the  internal  elec- 
tro-currents must  compensate  one  another,  and  there- 
fore the  magnetism  of  a  body  is  supposed  to  arise  from 
a  superficial  current  of  electricity  constantly  circulating 
in  a  direction  perpendicular  to  the  axes  of  the  magnet; 
so  that  the  reciprocal  action  of  magnets,  and  all  the  phe- 
nomena of  electro-magnetism,  are  reduced  to  the  action 
and  reaction  of  superficial  currents  of  electricity  acting 
at  right  angles  to  then*  direction.  Notwithstanding  the 
experiments  made  by  M.  Ampere  to  elucidate  the  sub- 
ject, there  is  still  an  uncertainty  in  the  theory  of  the 
induction  of  magnetism  by  an  electric  current  in  a  body 
near  it.  It  does  not  appear  whether  electric  currents 
which  did  not  previously  exist  are  actually  produced  by 
induction,  or  if  its  effects  be  only  to-  give  one  uniform 
direction  to  the  infinite  number  of  electric  currents  pre-  \ 
viously  existing  in  the  particles  of  the  body,  and  thus 
rendering  them  capable  of  exhibiting  magnetic  phenom- 
ena, in  the  same  manner  as  polarization  reduces  those 
undulations  of  light  to  one  plane  which  had  previously 
been  performed  in  every  plane.  Possibly  both  may  be 
combined  in  producing  the  effect ;  for  the  action  of  an 
electric  current  may  not  only  give  a  common  direction 
to  those  already  existing,  but  may  also  increase  their 
intensity.  However  that  may  be,  by  assuming  that  the 
attraction  and  repulsion  of  the  elementary  portions  of 
electric  currents  vary  inversely  as  the  squares  of  the 
distances,  the  action  being  at  right  angles  to  the  direc- 
tion of  the  current,  it  is  found  that  the  attraction  and 
repulsion  of  a  current  of  indefinite  length  on  the  ele- 
mentary portion  of  a  parallel  current  at  any  distance 
from  it,  is  in  the  simple  ratio  of  the  shortest  distance 
between  them.  Consequently  the  reciprocal  action  of 
electric  currents  is  reduced  to  the  composition  and  res- 
olution of  forces,  so  that  the  phenomena  of  electro-mag- 
netism are  brought  under  the  laws  of  dynamics  by  the 
theory  of  M.  Ampere. 
21 


322  MAGflETO-ELECTrmCITY.  SECT.  XXXlli. 


SECTION  XXXIII. 

Magneto-Electricity— Volta-Electric  Induction— Magneto-Electric  Induc- 
tion— Identity  in  the  Action  of  Electricity  and  Magnetism— Description 
of  a  Magneto-Electric  Apparatus  and  its  Effects — Identity  of  Magnetism 
and  Electricity. 

FROM  the  law  of  action  and  reaction  being  equal  and 
contrary,  it  might  be  expected  that,  as  electricity  pow- 
erfully affects  magnets,  so,  conversely,  magnetism  ought 
to  produce  electrical  phenomena.  By  proving  this  veiy 
important  fact  from  the  following  series  of  interesting 
and  ingenious  experiments,  Dr.  Faraday  has  added 
another  branch  to  the  science,  which  he  has  named 
magneto-electricity.  A  great  quantity  of  copper  wire 
was  coiled  in  the  form  of  a  helix  round  one  half  of  a 
ring  of  soft  iron,  and  connected  with  a  galvanic  battery  ; 
while  a  similar  helix  connected  with  a  galvanometer  was 
wound  round  the  other  half  of  the  ring,  but  not  touching 
the  first  helix.  As  soon  as  contact  was  made  with  the 
battery,  the  needle  of  the  galvanometer  was  deflected. 
But  the  action  was  transitory ;  for  when  the  contact 
was  continued,  the  needle  returned  to  its  usual  position, 
and  was  not  affected  by  the  continual  flow  of  the  electri- 
city through  the  wire  connected  with  the  battery.  As 
soon  however  as  the  contact  was  broken,  the  needle  of 
the  galvanometer  was  again  deflected,  but  in  the  con- 
trary direction.  Similar  effects  were  produced  by  an 
apparatus  consisting  of  two  helices  of  copper  wire  coiled 
round  a  block  of  wood,  instead  of  iron,  from  which  Dr. 
Faraday  infers  that  the  electric  current  passing  from  the 
battery  through  one  wire,  induces  a  similar  current 
through  the  other  wire,  but  only  at  the  instant  of  con- 
tact, and  that  a  momentary  current  is  induced  in  a  con- 
trary direction  when  .the  passage  of  the  electricity  is 
suddenly  interrupted.  These  brief  currents  or  waves 
of  electricity  were  found  to  be  capable  of  magnetizing 
needles,  of  passing  through  a  small  extent  of  fluid,  and 
when  charcoal  points  were  interposed  in  the  current  of 
the  induced  helix,  a  minute  spark  was  perceived  as  often 


S*cr.  XXXlil.     VOLTA-ELECTllHJ  INDUCTION.  3^3 

as  the  contacts  were  made  or  broken,  but  neither  chem- 
ical action  nor  any  other  electric  effects  were  obtained. 
A  deviation  of  the  needle  of  the  galvanometer  took  place 
when  common  magnets  were  employed  instead  of  the 
Voltaic  current;  so  that  the  magnetic  and  electric 
fluids  are  identical  in  their  effects  in  this  experiment. 
Again,  when  a  helix  formed  of  220  feet  of  copper  wire, 
into  which  a  cylinder  of  soft  iron  was  introduced,  was 
placed  between  the  north  and  south  poles  of  two  bar 
magnets,  and  connected  with  the  galvanometer  by  means 
of  wires  from  each  extremity,  as  often  as  the  magnets 
were  brought  into  contact  with  the  iron  cylinder,  it  be- 
came magnetic  by  induction,  and  produced  a  deflection 
in  the  needle  of  the  galvanometer.  On  continuing  the 
contact,  the  needle  resumed  its  natural  position,  and 
when  the  contact  was  broken,  deflection  took  place  in 
the  opposite  direction ;  when  the  magnetic  contacts 
were  reversed,  the  deflection  was  reversed  also.  With 
strong  magnets,  so  powerful  was  the  action,  that  the 
needle  of  the  galvanometer  whirled  round  several  times 
successively ;  and  similar  effects  were  produced  by  the 
mere  approximation  or  removal  of  the  heb'x  to  the  poles 
of  the  magnets.  Thus  it  was  proved  that  magnets  pro- 
duce the  veiy  same  effects  on  the  galvanometer  that 
electricity  does.  Though  at  that  time  no  chemical  de- 
composition was  effected  by  these  momentary  currents 
which  emanate  from  the  magnets,  they  agitated  the 
limbs  of  a  frog ;  and  Dr.  Faraday  justly  observes,  that 
"an  agent  which  is  conducted  along  metallic  wires  in 
the  manner  described,  which,  while  so  passing,  pos- 
sesses the  peculiar  magnetic  actions  and  force  of  a  cur- 
rent of  electricity,  which  can  agitate  and  convulse  the 
limbs  of  a  frog,  and  which  finally  can  produce  a  spark 
by  its  discharge  through  charcoal,  can  only  be  electri- 
city." Hence  it  appears  that  electrical  currents  are 
evolved  by  magnets,  which  produce  the  same  phenomena 
with  the  electrical  currents  from  the  Voltaic  battery : 
they  however  differ  materially  in  this  respect — that 
time  is  required  for  the  exercise  of  the  magnetico-elec- 
trie  induction,  whereas  Volta-electric  induction  is  in- 
stantaneous. 

After  Dr.  Faraday  had  proved  the  identity  of  the 


324  MAGNETO-ELECTRIC  APPARATUS.    SECT.  XXXII. 

magnetic  and  electric  fluids  by  producing  the  spark, 
heating  metallic  wires,  and  accomplishing  chemical 
decompositions,  it  was  easy  to  increase  these  effects  by 
more  powerful  magnets  and  other  arrangements.  The 
apparatus  now  in  use  is  in  effect  a  battery  where  the 
agent  is  the  magnetic  instead  of  the  Voltaic  fluid,  or  in 
other  words,  electricity,  and  is  thus  constructed. 

A  very  powerful  horseshoe  magnet,  formed  of  twelve 
steel  plates  in  close  approximation,  is  placed  in  a  hori- 
zontal position.  An  armature,  consisting  of  a  bar  of  the 
purest  soft  iron,  has  each  of  its  ends  bent  at  right 
angles,  so  that  the  faces  of  those  ends  may  be  brought 
directly  opposite  and  close  to  the  poles  of  the  magnet 
when  required.  Ten  copper  wires — covered  with  silk, 
in  order  to  insulate  them — are  wound  round  one  half  of 
the  bar  of  soft  iron,  as  a  compound  helix:  ten  other 
wires,  also  insulated,  are  wound  round  the  other  half  of 
the  bar.  The  extremities  of  the  first  set  of  wires  are  in 
metallic  connection  with  a  circular  disc,  which  dips  into 
a  cup  of  mercury,  while  the  ends  of  the  other  ten  wires 
in  the  opposite  direction  are  soldered  to  a  projecting 
screw-piece,  which  carries  a  slip  of  copper  with  two 
opposite  points.  The  steel  magnet  is  stationary ;  but 
when  the  armature,  together  with  its  appendages,  is 
made  to  rotate  vertically,  the  edge  of  the  disc  always 
remains  immersed  in  the  mercury,  while  the  points  of 
the  copper  slip  alternately  dip  in  it  and  rise  above  it. 
By  the  ordinary  laws  of  induction,  the  armature  becomes 
a  temporary  magnet  while  its  bent  ends  are  opposite 
the  poles  of  the  steel  magnet,  and  ceases  to  be  magnetic 
when  they  are  at  right  angles  to  them.  It  imparts  its 
temporaiy  magnetism  to  the  helices  which  concentrate 
it ;  and  while  one  set  conveys  a  current  to  the  disc,  the 
other  set  conducts  the  opposite  current  to  the  copper  slip. 
As  the  edge  of  the  revolving  disc  is  always  immersed  in 
the  mercury,  one  set  of  wires  is  constantly  maintained 
in  contact  with  it,  and  the  circuit  is  only  completed 
when  a  point  of  the  copper  slip  dips  in  the  mercury 
also  ;  but  the  circuit  is  broken  the  moment  that  point 
rises  above  it.  Thus,  by  the  rotation  of  the  armature, 
the  circuit  is  alternately  broken  and  renewed ;  and  as 
it  is  only  at  these  moments  that  electric  action  is  mani- 


SECT.  XXXIV.    ELECTRICITY  FROM  ROTATION.  325 

Tested,  a  brilliant  spark  takes  place  every  time  the  cop- 
per point  leaves  the  surface  of  the  mercury.  Platina 
wire  is  ignited,  shocks  smarts  enough  to  be  disagreeable 
are  given,  and  water  is  decomposed  with  astonishing 
rapidity  by  the  same  means;  which  proves  beyond  a 
doubt  the  identity  of  the  magnetic  and  electric  agencies, 
and  places  Dr.  Faraday,  whose  experiments  established 
the  principle,  in  the  first  rank  of  experimental  philoso- 
phers. 


SECTION  XXXIV. 

Electricity  produced  by  Rotation — Direction  of  the  Currents — Electricity 
from  the  Rotation  of  a  Magnet — M.  Arago's  Experiment  explained — 
Rotation  of  a  Plate  of  Iron  between  the  Poles  of  a  Magnet — Relation  of 
Substances  to  Magnets  of  three  kinds — Thermo- Electricity. 

M.  ARAGO  discovered  an  entirely  new  source  of  mag- 
netism in  rotatory  motion.  If  a  circular  plate  of  copper 
be  made  to  revolve  immediately  above  or  below  a  mag- 
netic needle  or  magnet,  suspended  in  such  a  manner 
that  the  magnet  may  rotate  in  a  plane  parallel  to  that  of 
the  copper  plate,  the  magnet  tends  to  follow  the  circum- 
volution of  the  plate ;  or  if  the  magnet  revolves,  the 
plate  tends  to  follow  its  motion  :  so  powerful  is  the 
effect,  that  magnets  and  plates  of  many  pounds  weight 
have  been  carried  round.  This  is  quite  independent  of 
the  motion  of  the  air,  since  it  is  the  same  when  a  pane 
of  glass  is  interposed  between  the  magnet  and  the  cop- 
per. When  the  magnet  and  the  plate  are  at  rest,  not 
the  smallest  effect,  attractive,  repulsive,  or  of  any  kind, 
can  be  perceived  between  them.  In  describing  this 
phenomenon,  M.  Arago  states  that  it  takes  place  not 
only  with  metals,  but  with  all  substances,  solids,  liquids, 
and  even  gases,  although  the  intensity  depends  upon 
the  kind  of  substance  in  motion.  Experiments  made 
by  Dr.  Faraday  explain  this  singular  action.  A  plate 
of  copper,  twelve  inches  in  diameter  and  one-fifth  of  an 
inch  thick,  was  placed  between  the  poles  of  a  powerful 
horseshoe  magnet,  and  connected  at  certain  points  with 
a  galvanometer  by  copper  wires.  When  the  plate  was 
at  rest  no  effect  was  produced  ;  but  as  soon  as  the  plate 
EE 


326  DIRECTION  OF  THE  CURRENTS    SECT.  XXXIV. 

was  made  to  revolve  rapidly,  the  galvanometer  needle 
was  deflected  sometimes  as  much  as  90°,  and,  by  a  uni- 
form rotation,  the  deflection  was  constantly  maintained 
at  45°.  When  the  motion  of  the  copper  plate  was  je- 
versed,  the  needle  was  deflected  in  the  contrary  direc- 
tion, and  thus  a  permanent  current  of  electricity  was 
evolved  by  an  ordinary  magnet.  The  intensity  of  the 
electricity  collected  by  the  wires,  and  conveyed  by  them 
to  the  galvanometer,  varied  with  the  position  of  the 
plate  relatively  to  the  poles  of  the  magnet. 

The  motion  of  the  electricity  in  the  copper  plate  may 
be  conceived  by  considering,  that  merely  by  moving  a 
single  wire  like  the  spoke  of  a  wheel  before  a  magnetic 
pole,  a  current  of  electricity  tends  to  flow  through  it 
from  one  end  to  the  other.  Hence,  if  a  wheel  be  con- 
structed of  a  great  many  such  spokes,  and  revolved 
near  the  pole  of  a  magnet  in  the  manner  of  the  copper 
disc,  each  radius  or  spoke  will  tend  to  have  a  current 
produced  in  it  as  it  passes  the  pole.  Now,  as  the 
circular  plate  is  nothing  more  than  an  infinite  number 
of  radii  or  spokes  in  contact,  the  currents  will  flow  in 
the  direction  of  the  radii  if  a  channel  be  open  for  their 
return,  and  in  a  continuous  plate  that  channel  is  afforded 
by  the  lateral  portions  on  each  side  of  the  particular 
radius  close  to  the  magnetic  pole.  This  hypothesis  is 
confirmed  by  observation,  for  the  currents  of  positive 
electricity  set  from  the  center  to  the  circumference,  and 
the  negative  from  the  circumference  to  the  center,  and 
vice  versa,  according  to  the  position  of  the  magnetic 
poles  and  the  direction  of  rotation.  So  that  a  collecting 
wire  at  the  center  of  the  copper  plate  conveys  positive 
electricity  to  the  galvanometer  in  one  case,  and  negative 
in  another ;  that  collected  by  a  conducting  wire  in  con- 
tact with  the  circumference  of  the  plate  is  always  the 
opposite  of  the  electricity  conveyed  from  the  center. 
It  is  evident  that  when  the  plate  and  magnet  are  both 
at  rest,  no  effect  takes  place,  since  the  electric  currents 
which  cause  the  deflection  of  the  galvanometer  cease 
altogether.  The  same  phenomena  may  be  produced  by 
electro-magnets.  The  effects  are  similar  when  the 
magnet  rotates  and  the  plate  remains  at  rest.  When 
the  magnet  revolves  uniformly,  about  its  own  axis,  elec- 


SECT.  XXXIV.   DIRECTION  OF  THE  CURRENTS.  327 

tricity  of  the  same  kind  is  collected  at  its  poles,  and  the 
opposite  electricity  at  its  equator. 

The  phenomena  which  take  place  in  M.  Arago's 
experiments  may  be  explained  on  this  principle.  When 
both  the  copper  plate  and  the  magnet  are  revolving,  the 
action  of  the  induced  electric  current  tends  continually 
to  diminish  then*  relative  motion,  and  to  bring  the  mov- 
ing bodies  into  a  state  of  relative  rest :  so  that  if  one  be 
made  to  revolve  by  an  extraneous  force,  the  other  will 
tend  to  revolve  about  it  in  the  same  direction,  and  with 
the  same  velocity. 

When  a  plate  of  iron,  or  of  any  substance  capable  of 
being  made  either  a  temporary  or  permanent  magnet, 
revolves  between  the  poles  of  a  magnet,  it  is  found  that 
dissimilar  poles  on  opposite  sides  of  the  plate  neutralize 
each  other's  effects,  so  that  no  electricity  is  evolved; 
while  similar  poles  on  each  side  of  the  revolving  plate 
increase  the  quantity  of  electricity,  and  a  single  pole 
end-on  is  sufficient.  But  when  copper,  and  substances 
not  sensible  to  ordinary  magnetic  impressions,  revolve, 
similar  poles  on  opposite  sides  of  the  plate  neutralize 
each  other;  dissimilar  poles  on  each  side  exalt  the 
action :  and  a  single  pole  at  the  edge  of  the  revolving 
plate,  or  end-on,  does  nothing.  This  forms  a  test  for 
distinguishing  the  ordinary  magnetic  force  from  that 
produced  by  rotation.  If  unlike  poles,  that  is,  a  north 
and  south  pole,  produce  more  effect  than  one  pole,  the 
force  will  be  due  to  electric  currents ;  if  similar  poles 
produce  more  effect  than  one,  then  the  power  is  not 
electric.  These  investigations  show  that  there  are 
really  very  few  bodies  magnetic  in  the  manner  of  iron. 
Dr.  Faraday  therefore  arranges  substances  in  three 
classes,  with  regard  to  their  relation  to  magnets  : — those 
affected  by  the  magnet  when  at  rest,  like  iron,  steel, 
and  nickel,  which  possess  ordinary  magnetic  properties ; 
those  affected  when  in  motion,  in  which  electric  cur- 
rents are  evolved  by  the  inductive  force  of  the  magnet, 
such  as  copper ;  and,  lastly,  those  which  are  perfectly 
indifferent  to  the  magnet,  whether  at  rest  or  in  motion. 

It  has  already  been  observed,  that  three  bodies  are 
requisite  to  form  a  galvanic  circuit,  one  of  which  must 
be  fluid.  But  in  1822,  Professor  Seebeck,  of  Berlin, 


328  THERMO-ELECTRICITY.  SECT.  XXXIV- 

discovered  that  electric  currents  may  be  produced  by 
the  partial  application  of  heat  to  a  circuit  formed  of  two 
solid  conductors.  For  example,  when  a  semicircle  of 
bismuth,  joined  to  a  semicircle  of  antimony,  so  as  to  form 
a  ring,  is  heated  at  one  of  the  junctions  by  a  lamp,  a 
current  of  electricity  flows  through  the  circuit  from  the 
antimony  to  the  bismuth,  and  such  thermo-electric  cur- 
rents produce  all  the  electro-magnetic  effects.  A  com- 
pass needle  placed  either  within  or  without  the  circuit, 
and  at  a  small  distance  from,  it,  is  deflected  from  its  na- 
tural position,  in  a  direction  corresponding  to  the  way  in 
which  the  electricity  is  flowing.  If  such  a  ring  be  sus- 
pended so  as  to  move  easily  in  any  direction,  it  will  obey 
the  action  of  a  magnet  brought  near  it,  and  may  even 
be  made  to  revolve.  According  to  the  researches  of  M. 
Seebeck,  the  same  substance,  unequally  heated,  exhibits 
electrical  currents ;  and  M.  Nobili  observed,  that  in  all 
metals,  except  zinc,  iron,  and  antimony,  the  electricity 
flows  from  the  hot  part  toward  that  which  is  cold.  That 
philosopher  attributes  terrestrial  magnetism  to  a  differ- 
ence in  the  action  of  heat  on  the  various  substances  of 
which  the  crust  of  the  earth  is  composed  ;  and  in  con- 
firmation of  his  views  he  has  produced  electrical  currents 
by  the  contact  of  two  pieces  of  moist  clay,  of  which  one 
was  hotter  than  the  other. 

M.  Becquerel  constructed  a  thermo-electric  battery  of 
one  kind  of  metal,  by  which  he  has  determined  the  re- 
lation between  the  heat  employed  and  the  intensity  of 
the  resulting  electricity.  He  found  that  in  most  metals 
the  intensity  of  the  current  increases  with  the  heat  to  a 
certain  limit,  but  that  this  law  extends  much  farther  in 
metals  that  are  difficult  to  fuse,  and  which  do  not  rust. 
The  experiments  of  Professor  Gumming  show  that  the 
mutual  action  of  a  magnet  and  a  thermo-electric  current 
is  subject  to  the  same  laws  as  those  of  magnets  and  gal- 
vanic currents,  consequently  all  the  phenomena  of  repul- 
sion, attraction,  and  rotation  maybe  exhibited  by  a  thermo- 
electric current.  M.  Botto,  of  Turin,  has  decomposed 
water  and  some  solutions  by  thermo-electricity ;  and 
very  recently  the  Cav.  Antinori  of  Florence  has  suc- 
ceeded in  obtaining  a  brilliant  spark  with  the  aid  of  an 
electro-dynamic  coil. 


SECT.  XXXV.        TERRESTRIAL  MAGNETISM.  329 

The  principle  of  thermo-electricity  has  been  employed 
by  MM.  Nobili  and  Melloni  for  measuring  extremely 
minute  quantities  of  heat  in  their  experiments  on  the 
instantaneous  transmission  of  radiant  caloric.  The 
thermo-rnultiplier,  which  they  constructed  for  that  pur- 
pose, consists  of  a  series  of  alternate  bars,  or  rather  fine 
wires  of  bismuth  and  antimony,  placed  side  by  side,  and 
the  extremities  alternately  soldered  together.  When 
heat  is  applied  to  one  end  of  this  apparatus,  the  other 
remaining  at  its  natural  temperature,  currents  of  elec- 
tricity flow  through  each  pair  of  bars,  which  are  conveyed 
by  wires  to  a  delicate  galvanometer,  the  needle  of  which 
points  out  the  intensity  of  the  electricity  conveyed,  and 
consequently  that  of  the  heat  employed.  This  instru- 
ment is  so  delicate  that  the  comparative  warmth  of  dif- 
ferent insects  has  been  ascertained  by  means  of  it. 


SECTION  XXXV. 

The  Action  of  Terrestrial  Magnetism  upon  Electric  Currents — Induction 
of  Electric  Currents  by  Terrestrial  Magnetism— The  Earth  Magnetic  by 
Induction — Mr.  Barlow's  Experiment  of  an  Artificial  Sphere — The  Heat 
of  the  Sun  the  Probable  Cause  of  Electric  Currents  in  the  Crust  of  the 
Earth  ;  and  of  the  Variations  in  Terrestrial  Magnetism — Electricity  of 
Metallic  Veins — Terrestrial  Magnetism  possibly  owing  to  Rotation — 
Magnetic  Properties  of  the  Celestial  Bodies— Identity  of  the  Five  Kinds 
of  Electricity — Connection  between  Light,  Heat,  and  Electricity  or  Mag- 
netism. 

IN  all  the  experiments  hitherto  described,  artificial 
magnets  alone  were  used ;  but  it  is  obvious  that  the 
magnetism  of  the  terrestrial  spheroid,  which  has  so 
powerful  an  influence  on  the  mariner's  compass,  must 
also  affect  electrical  currents.  It  consequently  appears 
that  a  piece  of  copper  wire  bent  into  a  rectangle,  and 
free  to  revolve  on  a  vertical  axis,  arranges  itself  with  its 
plane  at  right  angles  to  the  magnetic  meridian,  as  soon 
as  a  stream  of  electricity  is  sent  through  it.  Under  the 
same  circumstances  a  similar  rectangle,  suspended  on  a 
horizontal  axis  at  right  angles  to  the  magnetic  meridian, 
assumes  the  same  inclination  with  the  dipping  needle ; 
so  that  terrestrial  magnetism  has  the  same  influence  on 
electrical  currents  as  an  artificial  magnet.  But  the 
magnetic  action  of  the  earth  also  induces  electric  cur- 

E  E2 


330  EARTH  MAGNETIC  BY  INDUCTION.  SECT.  XXXV. 

rents.  When  a  hollow  helix  of  copper  wire,  whose 
extremities  are  connected  with  the  galvanometer,  is 
placed  in  the  magnetic  dip,  and  suddenly  inverted  sev- 
eral times,  accommodating  the  motion  to  the  oscillations 
of  the  needle,  the  latter  is  soon  made  to  vibrate  through 
an  arc  of  80°  or  90°.  Hence  it  is  evident,  that  what- 
ever may  be  the  cause  of  terrestrial  magnetism,  it  pro- 
duces currents  of  electricity  by  its  direct  inductive  power 
upon  a  metal  not  capable  of  exhibiting  any  of  the  ordi- 
nary magnetic  properties.  The  action  on  the  galvanom- 
eter is  much  greater  when  a  cylinder  of  soft  iron  is 
inserted  into  the  helix,  and  the  same  results  follow  the 
simple  introduction  of  the  iron  cylinder  into,  or  removal 
out  of,  the  helix.  These  effects  arise  from  the  iron 
being  made  a  temporary  magnet  by  the  inductive  action 
of  terrestrial  magnetism  ;  for  a  piece  of  iron,  such  as  a 
poker,  becomes  a  magnet  for  the  time,  when  placed  in 
the  line  of  the  magnetic  dip. 

M.  Biot  has  formed  a  theory  of  terrestrial  magnetism 
upon  the  observations  of  M.  de  Humboldt  as  data.  As- 
suming that  the  action  of  two  opposite  magnetic  poles 
of  the  earth  upon  any  point  is  inversely  as  the  squares 
of  the  distances,  he  obtains  a  general  expression  for  the 
direction  of  the  magnetic  needle,  depending  upon  the 
distance  between  the  north  and  south  magnetic  poles ; 
so  that  if  one  of  these  quantities  varies,  the  correspond-1 
ing  variation  of  the  other  will  be  known.  By  making 
the  distance  between  the  poles  vary,  and  comparing  the 
resulting  direction  of  the  needle  with  the  observations 
of  M.  de  Humboldt,  he  found  that  the  nearer  the  poles 
are  supposed  to  approach  to  one  another,  the  more  the 
computed  and  observed  results  agree ;  and  when  the 
poles  were  assumed  to  coincide,  or  nearly  so,  the  differ- 
ence between  theory  and  observation  is  the  least  possi- 
ble. It  is  evident,  therefore,  that  the  earth  does  not 
act  as  if  it  were  a  permanently  magnetic  body,  the  dis- 
tinguishing characteristic  of  which  is,  to  have  two  poles 
at  a  distance  from  one  another.  Mr.  Barlow  has  inves- 
tigated this  subject  with  much  skill  and  success.  He 
first  proved  that  the  magnetic  power  of  an  iron  sphere 
resides  in  its  surface  ;  he  then  inquired  what  the  super- 
ficial action  of  an  iron  sphere  in  a  state  of  transient  mag- 


SECT.  XXXV.  THE  EARTH  NOT  A  REAL  MAGNET.  331 

netic  induction,  on  a  magnetized  needle,  would  be,  if 
insulated  from  the  influence  of  terrestrial  magnetism. 
The  results  obtained,  corroborated  by  the  profound 
analysis  of  M.  Poisson,  on  the  hypothesis  of  the  two 
poles  being  indefinitely  near  the  center  of  the  sphere, 
are  identical  with  those  obtained  by  M.  Biot  for  the 
earth  from  M.  de  Humboldt's  observations.  Whence 
it  follows,  that  the  laws  of  terrestrial  magnetism  deduced 
from  the  formulae  of  M.  Biot,  are  inconsistent  with  those 
which  belong  to  a  permanent  magnet,  but  that  they  are 
perfectly  concordant  with  those  belonging  to  a  body  in  a 
state  of  transient  magnetic  induction.  The  earth,  there- 
fore, is  to  be  considered  as  only  transiently  magnetic  by 
induction,  and  not  a  real  magnet.  Mr.  Barlow  has  ren- 
dered this  extremely  probable  by  forming  a  wooden 
globe,  with  grooves  admitting  of  a  copper  wire  being 
coiled  round  it  parallel  to  the  equator  from  pole  to  pole. 
When  a  current  of  electricity  was  sent  through  the 
wire,  a  magnetic  needle  suspended  above  the  globe,  and 
neutralized  from  the  influence  of  the  earth's  magnetism, 
exhibited  all  the  phenomena  of  the  dipping  and  varia- 
tion needles,  according  to  its  positions  with  regard  to 
the  wooden  globe.  As  there  can  be  no  doubt  that  the 
same  phenomena  would  be  exhibited  by  currents  of 
thermo,  instead  of  Voltaic  electricity,  if  the  grooves  of 
the  wooden  globe  were  filled  by  rings  constituted  of  two 
metals,  or  of  one  metal  unequally  heated,  it  seems  highly 
probable  that  the  heat  of  the  sun  may  be  a  great  agent 
in  developing  electric  currents  in  or  near  the  surface  of 
earth,  by  its  action  upon  the  substances  of  which  the 
globe  is  composed,  and  by  changes  in  its  intensity,  may 
occasion  the  diurnal  variation  of  the  compass,  and  the 
other  vicissitudes  in  terrestrial  magnetism  evinced  by 
the  disturbance  in  the  direction  of  the  magnetic  lines,  in 
the  same  manner  as  it  influences  the  parallelism  of  the 
isothermal  lines.  That  such  currents  do  exist  in  metal- 
liferous veins  appears  from  the  experiments  of  Mr.  Fox 
in  the  Cornish  mines.  Even  since  the  last  edition  of 
this  book  was  published,  Mr.  Fox  has  obtained  additional 
proof  of  the  activity  of  electro-magnetism  under  the 
earth's  surface.  He  has  shown  that  not  only  the  nature 
of  the  metalliferous  deposits  must  have  been  determined 


332  EARTH  MAGNETIC  BY  ROTATION.    SECT.  XXXV. 

by  their  relative  electrical  conditions,  but  that  the  direc- 
tion of  the  metallic  veins  must  have  been  influenced  by 
the  direction  of  the  magnetic  meridians ;  and  in  fact 
almost  all  the  metallic  deposits  in  the  world  tend  from 
east  to  west,  or  from  northeast  to  southwest.  Though 
it  is  impossible  to  say  in  the  present  state  of  our  knowl- 
edge, how  far  the  sun  may  be  concerned  in  the  phe- 
nomena of  terrestrial  magnetism,  it  is  probable  that  the 
secular  and  periodic  disturbances  in  the  magnetic  force 
are  occasioned  by  a  variety  of  other  combining  circum- 
stances. Among  these  M.  Biot  mentions  the  vicinity  of 
mountain  chains  to  the  place  of  observation,  and  still 
more  the  action  of  extensive  volcanic  fires,  which  change 
the  chemical  state  of  the  terrestrial  surface,  they  them- 
selves varying  from  age  to  age,  some  becoming  extinct, 
while  others  burst  into  activity.  Should  the  ethereal 
medium  which  fills  space  be  the  same  with  the  electric 
fluid,  as  M.  Mossotti. supposes,  may  not  the  heat  of  the 
sun  rarefy  it  at  the  earth's  equator,  and  thus  by  the  in- 
equality of  its  distribution,  and  its  superior  density  at 
the  poles,  occasion  some  of  the  magnetic  phenomena  of 
the  globe  ?  and  may  not  the  sun's  motion  in  decimation 
cause  temporary  variations  of  density  in  the  fluid,  and 
produce  periodic  changes  in  the  magnetic  equator  and 
intensity  ?  Were  this  the  case,  all  the  planets  would 
be  magnets  like  the  earth,  being  precisely  in  similar  cir- 
cumstances. 

It  is  moreover  probable,  that  terrestrial  magnetism 
may  be  owing,  in  a  certain  extent,  to  the  earth's  rota- 
tion. Dr.  Faraday  has  proved  that  all  the  phenomena 
of  revolving  plates  may  be  produced  by  the  inductive 
action  of  the  earth's  magnetism  alone.  If  a  copper  plate 
be  connected  with  a  galvanometer  by  two  copper  wires, 
one  from  the  center  and  another  from  the  circumference, 
in  order  to  collect  and  convey  the  electricity,  it  is  found 
that  when  the  plate  revolves  in  a  plane  passing  through 
the  line  of  the  dip,  the  galvanometer  is  not  affected. 
But  as  soon  as  the  plate  is  inclined  to  that  plane,  elec- 
tricity begins  to  be  developed  by  its  rotation  ;  it  becomes 
more  powerful  as  the  inclination  increases,  and  arrives 
at  a  maximum  when  the  plate  revolves  at  right  angles  to 
the  line  of  the  dip.  When  the  revolution  is  in  the  samo 


S«trr.  XXXV.  EARTH  MAGNETIC  BY  ROTATION.  333 

direction  with  that  of  the  hands  of  a  watch,  the  current 
of  electricity  flows  from  its  center  to  the  circumference  ; 
and  when  the  rotation  is  in  the  opposite  direction,  the 
current  sets  the  contrary  way.  The  greatest  deviation 
of  the  galvanometer  amounted  to  50°  or  60°,  when  the 
direction  of  the  rotation  was  accommodated  to  the  oscil- 
lations of  the  needle.  Thus  a  copper  plate,  revolving  in 
a  plane  at  right  angles  to  the  line  of  the  dip,  forms  a  new 
electrical  mnchine,  differing  from  the  common  plate- 
glass  machine,  by  the  material  of  which  it  is  composed 
being  the  most  perfect  conductor,  whereas  glass  is  the 
most  perfect  non-conductor ;  besides,  insulation,  which 
is  essential  in  the  glass  machine,  is  fatal  in  the  copper 
one.  The  quantity  of  electricity  evolved  by  the  metal 
does  not  appear  to  be  inferior  to  that  developed  by  the 
glass,  though  very  different  in  intensity. 

From  the  experiments  of  Dr.  Faraday,  and^lso  from 
theory,  it  is  possible  that  the  rotation  of  the  earth  may 
produce  electric  currents  in  its  own  mass.  In  that  case, 
they  would  flow  superficially  in  the  meridians,  and  if 
collectors  could  be  applied  at  the  equator,  and  poles,  as 
in  the  revolving  plate,  negative  electricity  would  be  col- 
lected at  the  equator,  and  positive  at  the  poles ;  that  is 
to  say,  there  would  be  a  deficiency  at  the  equator  and  a 
redundancy  at  the  poles  ;  but  without  something  equiv- 
alent to  conductors  to  complete  the  circuit,  these  cur- 
rents could  not  exist. 

Since  the  motion,  not  only  of  metals  but  even  of  fluids, 
when  under  the  influence  of  powerful  magnets,  evolves 
electricity,  it  is  probable  that  the  gulf-stream  may  exert 
a  sensible  influence  upon  the  forms  of  the  lines  of  mag- 
netic variation,  in  consequence  of  electric  currents  mov- 
ing across  it,  by  the  electro-magnetic  induction  of  the 
earth.  Even  a  ship,  passing  over  the  surface  of  the 
water  in  northern  or  southern  latitudes,  ought  to  have 
electric  currents  running  directly  across  the  line  of  her 
motion.  Dr.  Faraday  observes,  that  such  is  the  facility 
with  which  electricity  is  evolved  by  the  earth's  magnet- 
ism, that  scarce  any  piece  of  metal  can  be  moved  in 
contact  with  others  without  a  development  of  it,  and 
consequently,  among  the  arrangements  of  steam-engines 
and  metallic  machinery,  curious  electro-magnetic  coin- 


334  MAGNETISM  OF  SUN  AND  PLANETS.   SECT.  XXXV. 

binations  probably  exist,  which  have  never  yet  been  no- 
ticed. 

According  to  the  observations  of  MM.  Biot  and  Gay- 
Lussac,  during  their  aerostatic  expedition,  the  magnetic 
action  is  not  confined  to  the  surface  of  the  earth,  but 
extends  into  space.  The  moon  has  become  highly 
magnetic  by  induction,  in  consequence  of  her  proximity 
to  the  earth,  and  because  her  greatest  diameter  always 
points  toward  it.  Her  influence  on  terrestrial  magnetism 
is  now  ascertained  :  the  magnetism  of  the  hemisphere 
that  is  turned  toward  the  earth  attracts  the  pole  of  our 
needles  that  is  turned  toward  the  south,  and  increases 
the  magnetism  of  our  hemisphere  ;  and  as  the  magnetic, 
like  the  gravitating  force,  extends  through  space,  the 
induction  of  the  sun,  moon,  and  planets  must  occasion 
perpetual  variations  in  the  intensity  of  terrestrial  mag- 
netism, by  the  continual  changes  in  their  relative  posi- 
tions. 

Jn  the  brief  sketch  that  has  been  given  of  the  five 
kinds  of  electricity,  those  points  of  resemblance  have 
been  pointed  out  which  are  characteristic  of  one  indi- 
vidual power.  But  as  many  anomalies  have  been  lately 
removed,  and  the  identity  of  the  different  kinds  placed 
beyond  a  doubt  by  Dr.  Faraday,  it  may  be  satisfactory 
to  take  a  summary  view  of  the  various  coincidences  in 
their  modes  of  action  on  which  their  identity  has  been  so 
ably  and  completely  established  by  that  great  electrician. 

The  points  of  comparison  are  attraction  and  repulsion 
at  sensible  distances,  discharge  from  points  through  air, 
the  heating  power,  magnetic  influence,  chemical  decom- 
position, action  on  the  human  frame,  and  lastly,  the  spark. 

Ordinary  electricity  is  readily  discharged  from  points 
through  air,  but  Dr.  Faraday  found  that  no  sensible  ef- 
fect takes  place  from  a  Voltaic  battery  consisting  of  140 
double  plates,  either  through  air  or  in  the  exhausted 
receiver  of  an  air-pump,  the  tests  of  the  discharge  being 
the  electrometer  and  chemical  action,— a  circumstance 
owing  to  the  small  degree  of  tension,  for  an  enormous 
quantity  of  electricity  is  required  to  make  these  effects 
sensible,  and  for  that  reason  they  cannot  be  expected 
from  the  other  kinds,  which  are  much  inferior  in  de- 
gree. Common  electricity  passes  easily  through  rare- 


SstT.  XXXV.  IDENTITY  OF  THE  ELECTRICITIES.  335 

fied  and  hot  air,  and  also  through  flame.  Dr.  Faraday 
effected  chemical  decomposition  and  a  deflection  of  the 
galvanometer  by  the  transmission  of  Voltaic  electricity 
through  heated  air,  and  observes  that  these  experiments 
are  only  cases  of  the  discharge  which  takes  place  through 
air  between  the  charcoal  terminations  of  the  poles  of  a 
powerful  battery  when  they  are  gradually  separated 
after  contact — for  the  air  is  then  heated.  Sir  Humphry 
Davy  mentions  that,  with  the  original  Voltaic  apparatus 
at  the  Royal  Institution,  the  discharge  passed  through 
four  inches  of  air  ;  that,  in  the  exhausted  receiver  of  an 
air-pump,  the  electricity  would  strike  through  nearly 
half  an  inch  of  space,  and  the  combined  effects  of  rare- 
faction and  heat  upon  the  included  air  were  such  as  to 
enable  it  to  conduct  the  electricity  through  a  space  of  six 
or  seven  inches.  A  Leyden  jar  may  be  ^instantaneously 
charged  with  Voltaic,  and  also  with  magneto-electricity 
— another  proof  of  their  tension.  Such  effects  cannot  be 
obtained  frojn  the  other  kinds,  on  account  of  their  weak- 
ness only. 

The  heating  powers  of  ordinary  and  Voltaic  electri- 
city have  long  been  known,  but  the  world  is  indebted  to 
Dr.  Faraday  for  the  wonderful  discovery  of  the  heating 
power  of  the  magnetic  fluid  :  there  is  no  indication  of 
heat  either  from  the  animal  or  thermo  electricities.  All 
kinds  of  electricity  have  strong  magnetic  powers,  those 
of  the  Voltaic  fluid  are  highly  exalted,  and  the  existence 
of  the  magneto  and  thermo  electricities  was  discovered 
by  their  magnetic  influence  alone.  The  needle  has 
been  deflected  by  all  in  the  same  manner,  and  magnets 
have  been  made  by  all  according  to  the  same  laws. 
Ordinary  electricity  was  long  supposed  incapable  of  de- 
flecting the  needle  ;  M.  Colladon  and  Dr.  Faraday  how- 
ever have  proved  that,  in  this  respect  also,  ordinary  elec- 
tricity agrees  with  Voltaic,  but  that  time  must  be  allowed 
for  its  action.  It  deflected  the  needle,  whether  the  cur- 
rent was  sent  through  rarefied  ah-,  water,  or  wire. 
Numerous  chemical  decompositions  have  been  effected 
by  ordinary  and  Voltaic  electricity,  according  to  the 
same  laws  and  modes  of  arrangement.  Dr.  Davy  de- 
composed water  by  the  ejfictricity  of  the  torpedo, — Dr. 
Faraday  accomplished  its  decompositToii,  ancTTJrTRitchie 


336  IDENTITY  OF  THE  ELECTRICITIES.  SECT.  XXXV. 

its  composition,  by  means  of  magnetic,  action ;  and  M. 
Botto  of  Turin  has  shownHhe  chemical  effects  of  the 
thftfirua-pJer'.t-.rrcjty  in  the  decomposition  of  water,  and 
some  other  substances.  The*  elecjj^e  and  ggkMwic 
shock,  the  flash  in  the  eyes,  and~thesensation  on  the 
tongue,  are  well  known.  All  these  effects  are  produced 
by  magneto-electricity,  even  to  a  painful  degree.  The 
torpetfcTand  gyifmOTTTT^lectricus  give  severe  shocks,  and 
the  limbs  of  a  frog  have  been  convulsed  by  thermo-elec- 
tricity. The  last  point  of  comparison  is  the  spark, 
which  is  common  to  the  ordinary  Voltaic  and  magnetic 
fluids  ;  and  Professor  Linari,  of  Siena,  has  very  lately 
obtained  both  the  direct  and  induced  sparks  from  the 
torpedo,  proving  that  in  this  respect  aniraal_el££tricity 
does  not  differ  from  the  others.  Indeed,  the  conclusion 
drawn  by  Dr.  Faraday  is  that  the  five  kinds  of  electri- 
city are  identical,  and  that  the  differences  of  intensity 
and  quantity  are  quite  sufficient  to  account  for  what 
were  supposed  to  be  their  distinctive  qualities.  He  has 
given  still  greater  assurance  of  their  identity  by  showing 
that  the  magnetic  force  and  the  chemical  action  of  elec- 
tricity are  in  direct  proportion  to  the  absolute  quantity 
of  the  fluid  which  passes  through  the  galvanometer, 
whatever  its  intensity  may  be. 

In  light,  heat,  and  electricity,  or  magnetism,  nature 
has  exhibited  principles  which  do  not  occasion  any  ap- 
preciable change  in  the  weight  of  bodies,  although  their 
presence  is  manifested  by  the  most  remarkable  mechan- 
ical and  chemical  action.  These  agencies  are  so  con- 
nected, that  there  is  reason  to  believe  they  will  ulti- 
mately be  referred  to  some  one  power  of  a  higher  order, 
in  conformity  with  the  general  economy  of  the  system 
of  the  world,  where  the  most  varied  and  complicated 
effects  are  produced  by  a  small  number  of  universal 
laws.  These  principles  penetrate  matter  in  all  direc- 
tions ;  their  velocity  is  prodigious,  and  their  intensity 
varies  inversely  as  the  squares  of  the  distances.  The 
development  of  electric  currents,  as  well  by  magnetic 
as  electric  induction,  the  similarity  in  their  mode  of  ac- 
tion in  a  great  variety  of  circumstances,  but  above  all, 
the  production  of  the  spark  from  a  magnet,  the  ignition 
of  metallic  wires,  and  chemical  decomposition,  show  that 


SKCT.  XXXVI.  COMETS.  337 

magnetism  can  no  longer  be  regarded  as  a  separate  in- 
dependent principle.  Although  the  evolution  of  light 
and  heat  during  the  passage  of  the  electric  fluid  may  be 
from  the  compression  of  the  air,  yet  the  development 
of  electricity  by  heat,  the  influence  of  heat  on  magnetic 
bodies,  and  that  of  light  on  the  vibration  of  the  compass, 
show  an  occult  connection  between  all  these  agents, 
which  probably  will  one  day  be  revealed.  In  the  mean 
time  it  opens  a  noble  field  of  experimental  research  to 
philosophers  of  the  present,  perhaps  of  future  ages. 


SECTION  XXXVI. 

Ethereal  Medium— Comets— Do  not  disturb  the  Solar  System— Their 
Orbits  and  Disturbances— M.  Faye's  Comet,  probably  the  same  with 
Level's — Periods  of  other  three  known — Halley's— Acceleration  in  the 
Mean  Motions  of  Encke's  and  Biela's  Comets— The  Shock  of  a  Comet- 
Disturbing  Action  of  the  Earth  and  Planets  on  Encke's  and  Biela's 
Comets — Velocity  of  Comets — The  Great  Comet  of  1843 — Physical  Con- 
stitution— Shine  by  borrowed  Light — Estimation  of  their  Number. 

IN  considering  the  constitution  of  the  earth  and  the 
fluids  which  surround  it,  various  subjects  have  presented 
themselves  to  our  notice,  of  which  some,  for  aught  we 
know,  are  confined  to  the  planet  we  inhabit ;  some  are 
common  to  it  and  to  the  other  bodies  of  our  system. 
But  an  all-pervading  ether  probably  fills  the  whole  visi- 
ble creation,  and  conveys,  in  the  form  of  light,  tremors 
which  may  have  been  excited  in  the  deepest  recesses 
of  the  universe  thousands  of  years  before  we  were  called 
into  being.  The  existence  of  such  a  medium,  though 
at  first  hypothetical,  is  nearly  proved  by  the  undulatory 
theory  of  light,  and  rendered  all  but  certain  within  a 
few  years  by  the  motion  of  comets,  and  by  its  action 
upon  the  vapors  of  which  they  are  chiefly  composed. 
It  has  often  been  imagined,  that,  in  addition  to  the  ef- 
fects of  heat  and  electricity,  the  tails  of  comets  have 
infused  new  substances  into  our  atmosphere.  Possibly 
the  earth  may  attract  some  of  that  nebulous  matter, 
since  the  vapors  raised  by  the  sun's  heat,  when  the 
comets  are  in  perihelio,  and  which  form  their  tails,  are 
scattered  through  space  in  their  passage  to  their  aphe- 
lion ;  but  it  has  hitherto  produced  no  effect,  nor  have 
22  FF 


338  EARTH  NOT  AFFECTED  BY  COMETS.   SECT.XXXVI. 

the  seasons  ever  been  influenced  by  these  bodies.  The 
light  of  the  comet  of  the  year  1811,  which  was  so  bril- 
liant, did  not  impart  any  heat  even  when  condensed  on 
the  bulb  of  a  thermometer,  of  a  structure  so  delicate 
that  it  would  have  made  the  hundredth  part  of  a  degree 
evident.  In  all  probability,  the  tails  of  comets  may  have 
passed  over  the  earth  without  its  inhabitants  being  con- 
scious of  their  presence ;  and  there  is  reason  to  believe 
that  the  tail  of  the  great  comet  of  J1843  did  so. 

The  passage  of  comets  has  never  sensibly  disturbed 
the  stability  of  the  solar  system ;  their  nucleus,  being  in 
general  only  a  mass  of  vapor,  is  so  rare,  and  their  transit 
so  rapid,  that  the  time  has  not  been  long  enough  to  ad- 
mit of  a  sufficient  accumulation  of  impetus  to  produce  a 
perceptible  action.  Indeed  M.  Dusejour  has  proved, 
that  under  the  most  favorable  circumstances,  a  comet 
cannot  remain  longer  than  two  hours  and  a  half  at  a  less 
distance  from  the  earth  than  10,500  leagues.  The 
comet  of  1770  passed  within  about  six  times  the  distance 
of  the  moon  from  the  earth,  without  even  affecting  our 
tides.  According  to  La  Place,  the  action  of  the  earth 
on  the  comet  of  1770  augmented  the  period  of  its  revolu- 
tion by  more  than  two  days  ;  and  if  comets  had  any  per- 
ceptible disturbing  energy,  the  reaction  of  the  comet 
ought  to  have  increased  the  length  of  our  year.  Had 
the  mass  of  that  comet  been  equal  to  the  mass  of  the 
earth,  its  disturbing  action  would  have  increased  the 
length  of  the  sidereal  year  by  21'  53™ ;  but  as  Delainbre's 
computations  from  the  Greenwich  observations  of  the 
sun  show  that  the  length  of  the  year  has  not  been  in- 
creased by  the  fraction  of  a  second,  its  mass  could  not 
have  been  equal  to  the  ^l(T^th  part  of  that  of  the  earth. 
This  accounts  for  the  same  comet  having  twice  swept 
through  the  system  of  Jupiter's  satellites  without  de- 
ranging the  motion  of  these  moons.  M.  Dusejour  has 
computed  that  a  comet,  equal  in  mass  to  the  earth,  pass- 
ing at  the  distance  of  12,150  leagues  from  our  planet, 
would  increase  the  length  of  the  year  to  367lt  16h5'n,  and 
the  obliquity  of  the  ecliptic  as  much  as  2°.  So  the 
principal  action  of  comets  would  be  to  alter  the  calendar, 
even  if  they  were  dense  enough  to  affect  the  earth. 

Comets  traverse  all  parts  of  the  heavens ;  their  paths 


S«CT.  XXXVI.  ORBITS  OF  COMETS.  339 

have  every  possible  inclination  to  the  plane  of  the  eclip- 
tic, and,  unlike  the  planets,  the  motion  of  more  than 
half  of  those  that  have  appeared  has  been  retrograde, 
that  is,  from  east  to  west.  They  are  only  visible  when 
near  their  perihelia;  then  their  velocity  is  such,  that  its 
square  is  twice  as  great  as  that  of  a  body  moving  in  a 
circle  at  the  same  distance :  they  consequently  remain 
but  a  very  short  time  within  the  planetary  orbits.  And 
as  all  the  conic  sections  of  the  same  focal  distance  sen- 
sibly coincide,  through  a  small  arc,  on  each  side  of  the 
extremity  of  their  axis,  it  is  difficult  to  ascertain  in  which 
of  these  curves  the  comets  move,  from  observations 
made,  as  they  necessarily  must  be,  at  their  perihelia 
(N.  220).  Probably  they  all  move  in  extremely  eccen- 
tric ellipses;  although  in  most  cases  the  parabolic  curve 
coincides  most  nearly  with  their  observed  motions. 
Some  few  seem  to  describe  hyperbolas;  such,  being  once 
visible  to  us,  would  vanish  forever,  to  wander  through 
boundless  space,  to  the  remote  systems  of  the  universe. 
If  a  planet  be  supposed  to  revolve  in  a  circular  orbit,  the 
radius  of  which  is  equal  to  the  perihelion  distance  of  a 
comet  moving  in  a  parabola,  the  areas  described  by  these 
two  bodies  in  the  same  time  will  be  as  unity  to  the 
square  root  of  two,  which  forms  such  a  connection  be- 
tween the  motion  of  comets  and  planets,  that  by  Kep- 
ler's law,  the  ratio  of  the  areas  described  during  the 
same  time  by  the  comet  and  the  earth  may  be  found. 
So  that  the  place  of  a  comet  may  be  computed  at  any 
time  in  its  parabolic  orbit,  estimated  from  the  instant  of 
its  passage  at  the  perihelion.  It  is  a  problem  of  very 
great  difficulty  to  determine  all  the  other  elements  of 
parabolic  motion — namely,  the  comet's  perihelion  dis- 
tance, or  shortest  distance  from  the  sun,  estimated  in 
parts  of  the  mean  distance  of  the  earth  from  the  sun; 
the  longitude  of  the  perihelion ;  the  inclination  of  the 
orbit  on  the  plane  of  the  ecliptic ;  and  the  longitude  of 
the  ascending  node.  Three  observed  longitudes  and 
latitudes  of  a  comet  are  sufficient  for  computing  the  ap- 
proximate values  of  these  quantities;  but  an  accurate 
estimation  of  them  can  only  be  obtained  by  successive 
corrections,  from  a  number  of  observations,  distant  from 
one  another.  When  the  motion  of  a  comet  is  retrograde, 


340  PARABOLIC  ELEMENTS.  SECT.  XXXVI. 

tho  place  of  the  ascending  node  is  exactly  opposite  to 
what  it  is  when  the  motion  is  direct.  Hence  the  place 
of  the  ascending  node,  together  with  the  direction  of  the 
comet's  motion,  show  whether  the  inclination  of  the 
orbit  is  on  the  north  or  south  side  of  the  plane  of  the 
ecliptic.  If  the  motion  be  direct,  the  inclination  is  on 
the  north  side ;  if  retrograde,  it  is  on  the  south  side. 

The  identity  of  the  elements  is  the  only  proof  of  the 
return  of  a  comet  to  our  system.  Should  the  elements 
of  a  new  comet  be  the  same,  or  nearly  the  same,  with 
those  of  any  one  previously  known,  the  probability  of 
the  identity  of  the  two  bodies  is  very  great,  since  the 
similarity  extends  to  no  less  than  four  elements,  every 
one  of  which  is  capable  of  an  infinity  of  variations.  But 
even  if  the  orbit  be  determined  with  all  the  accuracy  the 
case  admits  of,  it  may  be  difficult,  or  even  impossible, 
to  recognize  a  comet  on  its  return,  because  its  orbit 
would  be  very  much  changed  if  it  passed  near  any  of 
the  large  planets  of  this  or  of  any  other  system,  in  con- 
sequence of  their  disturbing  energy,  which  would  be 
very  great  on  bodies  of  so  rare  a  nature. 

By  far  the  most  curious  and  interesting  instance  of 
the  disturbing  action  of  the  great  bodies  of  our  system 
is  found  in  the  comet  of  1770.  The  elements  of  its  or- 
bit, determined  by  Messier,  did  not  agree  with  those  of 
any  comet  that  had  hitherto  been  computed,  yet  Lexel 
ascertained  that  it  described  an  ellipse  about  the  sun, 
whose  major  axis  was.  only  equal  to  three  times  the 
length  of  the  diameter  of  the  terrestrial  orbit,  and  con- 
sequently that  it  must  return  to  the  sun  at  intervals  of 
five  years  and  a  half.  This  result  was  confirmed  by 
numerous  observations,  as  the  comet  was  visible  through 
an  arc  of  170°  ;  yet  this  comet  had  never  been  observed 
before  the  year  1770,  nor  has  it  ever  again  been  seen 
till  1843,  though  very  brilliant.  The  disturbing  action 
of  the  larger  planets  affords  a  solution  of  this  anomaly, 
as  Lexel  ascertained  that  in  1767  the  comet  must  have 
passed  Jupiter  at  a  distance  less  than  the  fifty-eighth 
part  of  its  distance  from  the  sun,  and  that  in  1779  it 
would  be  500  times  nearer  Jupiter  than  the  sun  ;  conse- 
quently the  action  of  the  sun  on  the  comet  would  not  be 
the  fiftieth  part  of  what  it  would  experience  from  Jupi- 


SECT.  XXXVI.  LEXEL'S  COMET.  341 

ter,  so  that  Jupiter  became  the  primum  mobile.  As- 
suming the  orbit  to  be  such  as  Lexel  had  determined  in 
1770,  La  Place  found  that  the  action  of  Jupiter,  previ- 
ous to  the  year  1770,  had  so  completely  changed  the 
form  of  it,  that  the  comet  which  had  been  invisible  to  us 
before  1770,  was  then  brought  into  view,  and  that  the 
action  of  the  same  planet  producing  a  contrary  effect, 
has  subsequently  to  that  year  removed  it  from  our  sight, 
since  it  was  computed  to  be  revolving  in  an  orbit  whose 
perihelion  was  beyond  the  orbit  of  Ceres.  However, 
the  action  of  Jupiter  during  the  summer  of  1840  must 
have  been  so  great,  from  his  proximity  to  that  singular 
body,  that  he  seems  to  have  brought  it  back  to  its  former 
path,  as  he  had  done  in  1767,  for  the  elements  of  the 
orbit  of  a  comet  which  was  discovered  in  November, 
1843,  by  M.  Faye,  agree  so  nearly  with  those  of  the 
orbit  of  Lexel's  comet  as  to  leave  scarcely  a  doubt  of 
their  identity.  From  the  smallness  of  the  eccentricity, 
the  orbit  resembles  those  of  the  planets,  but  this  comet 
is  liable  to  greater  perturbations  than  any  other  body  in 
the  system,  because  it  comes  very  near  the  orbit  of 
Mars  when  in  perihelion,  and  very  near  that  of  Jupiter 
when  in  aphelion ;  besides,  it  passes  within  a  compara- 
tively small  distance  of  the  orbits  of  the  minor  planets, 
and  as  it  will  continue  to  cross  the  orbit  of  Jupiter  at 
each  revolution  till  the  two  bodies  meet,  its  periodic 
time,  now  about  seven  years,  will  again  be  changed,  but 
in  the  mean  time  it  ought  to  return  to  its  perihelion  in 
the  year  1851.  This  comet  might  have  been  seen  from 
the  earth  in  1776,  had  its  light  not  been  eclipsed  by  that 
of  the  sun.  It  is  quite  possible  that  comets  frequenting 
our  system  may  be  turned  away,  or  others  brought  to 
the  sun,  by  the  attraction  of  planets  revolving  beyond 
the  orbit  of  Uranus,  or  by  bodies  still  farther  removed 
from  the  solar  influence. 

Other  three  comets,  liable  to  less  disturbance,  return 
to  the  sun  at  stated  intervals.  Halley  computed  the 
elements  of  the  orbit  of  a  comet  that  appeared  in  the 
year  1682,  which  agreed  so  nearly  with  those  of  the 
comets  of  1607  and  1531,  that  he  concluded  it  to  be  the 
same  body  returning  to  the  sun  at  intervals  of  about 
seventy-five  years.  He  consequently  predicted  its  re- 
FF2 


342  HALLEY'S  COMET.  SECT.  XXXVI. 

appearance  in  the  year  1758,  or  in  the  beginning  of 
1759.  Science  was  not  sufficiently  advanced  in  the  time 
of  Halley^  to  enable  him  to  determine  the  perturbations 
this  comet  might  experience ;  but  Clairaut  computed, 
that  in  consequence  of  the  attraction  of  Jupiter  and 
Saturn,  its  periodic  time  would  be  so  much  shorter  than 
during  its  revolution  between  1607  and  1682,  that  it 
would  pass  its  perihelion  on  the  18th  of  April,  1759. 
The  comet  did  arrive  at  that  point  of  its  orbit  on  the  12th 
of  March,  which  was  thirty-seven  days  before  the  time 
assigned.  Clairaut  subsequently  reduced  the  error  to 
twenty-three  days ;  and  La  Place  has  since  shown  that 
it  would  only  have  been  thirteen  days  if  the  mass  of 
Saturn  had  been  as  well  known  as  it  is  now.  It  appears 
from  this,  that  the  path  of  the  comet  was  not  quite  known 
at  that  period ;  and  although  many  observations  were 
then  made,  they  were  far  from  attaining  the  accuracy  of 
those  of  the  present  day.  Besides,  since  the  year  1759 
the  orbit  of  the  comet  has  been  altered  by  the  attraction 
of  Jupiter  in  one  direction,  and  that  of  the  earth,  Saturn, 
and  Uranus,  in  the  other;  yet,  notwithstanding  these 
sources  of  uncertainty,  and  our  ignorance  of  all  the  pos- 
sible causes  of  derangement  from  unknown  bodies  on 
the  confines  of  our  system,  or  in  the  regions  beyond  it, 
the  comet  has  appeared  exactly  at  the  time,  and  not  far 
from  the  place,  assigned  to  it  by  astronomers ;  and  its 
actual  arrival  at  its  perihelion  a  little  before  noon  on  the 
16th  of  November,  1835,  only  differed  from  the  com- 
puted time  by  a  veiy  few  days. 

The  fulfilment  of  this  astronomical  prediction  is  truly 
wonderful  if  it  be  considered  that  the  comet  is  seen  only 
for  a  few  weeks,  during  its  passage  through  our  system, 
and  that  it  wanders  from  the  sun  for  seventy-five  years 
to  twice  the  distance  of  Uranus.  This  enormous  orbit 
is  four  times  longer  than  it  is  broad ;  its  length  is  about 
3420  millions  of  miles,  or  about  thirty-six  times  the  mean 
distance  of  the  earth  from  the  sun.  At  its  perihelion 
the  comet  comes  within  nearly  fifty-seven  millions  of 
miles  of  the  sun,  and  at  its  aphelion  it  is  sixty  times 
more  distant.  On  account  of  this  extensive  range  it 
must  experience  3600  times  more  light  and  heat,  when 
nearest  to  the  sun  than  in  the  most  remote  point  of  its 


S«cr.  XXXVI.       HALLEY'S  COMET.  343 

orbit.  In  the  one  position  the  sun  will  seem  to  be  four 
times  larger  than  he  appears  to  us,  and  at  the  other  he 
will  not  be  apparently  larger  than  a  star  (N.  221). 

On  the  first  appearance  of  Halley's  comet,  early  in 
August,  1835,  it  seemed  to  be  merely  a  globular  mass  of 
dim  vapor,  without  a  tail.  A  concentration  of  light,  a 
little  on  one  side  of  the  center,  increased  as  the  comet 
approached  the  sun  and  earth,  and  latterly  looked  so 
like  the  disc  of  a  small  planet,  that  it  might  have  been 
mistaken  for  a  solid  nucleus.  M.  Struve,  however,  saw 
a  central  occultation  of  a  star  of  the  ninth  magnitude  by 
the  comet,  at  Dorpat,  on  the  29th  of  September.  The 
star  remained  constantly  visible,  without  any  considera- 
ble diminution  of  light ;  and  instead  of  being  eclipsed, 
the  nucleus  of  the  comet  disappeared  at  the  moment  of 
conjunction  from  the  brilliancy  of  the  star.  The  tail 
increased  as  the  comet  approached  its  perihelion,  and 
shortly  before  it  was  lost  in  the  sun's  rays,  it  was  between 
thirty  and  forty  degrees  in  length. 

According  to  the  observations  of  M.  Valz,  of  Nismes, 
the  nebulosity  increased  in  magnitude  as  it  approached 
the  sun  ;  but  no  other  comet  on  record  has  exhibited 
such  sudden  and  unaccountable  changes  of  aspect.  The 
nucleus,  clear  and  well  defined,  like  the  disc  of  a  planet, 
was  observed  on  one  occasion  to  become  obscure  and  en- 
larged hi  the  course  of  a  few  hours.  But  by  far  the 
most  remarkable  circumstance  was  the  sudden  appear- 
ance of  certain  luminous  brushes  or  sectors,  diverging 
from  the  center  of  the  nucleus  through  the  nebulosity. 
M.  Struve  describes  the  nucleus  of  the  comet,  in  the 
beginning  of  October,  as  elliptical,  and  like  a  burning 
coal,  out  of  which  there  issued,  in  a  direction  nearly  op- 
posite to  the  tail,  a  divergent  flame,  varying  in  intensity, 
form,  and  direction,  appearing  occasionally  even  double, 
and  suggesting  the  idea  of  luminous  gas  bursting  from 
the  nucleus.  On  one  occasion  M.  Arago  saw  three  of 
these  divergent  flames  on  the  side  opposite  the  tail,  rising 
through  the  nebulosity,  which  they  greatly  exceeded  in 
brilliancy  :  after  the  comet  had  passed  its  perihelion,  it 
acquired  another  of  these  luminous  fans,  which  was  ob- 
served by  Sir  John  Herschel  at  the  Cape  of  Good  Hope. 
Hevelius  describes  an  appearance  precisely  similar. 


344  HALLEY'S  COMET.  SECT.  XXXVI. 

which  he  had  witnessed  in  this  comet  at  its  approach  to 
the  sun  in  the  year  1682,  and  something  of  the  kind 
seems  to  have  been  noticed  in  the  comet  of  1744.  Pos- 
sibly the  second  tail  of  the  comet  of  1724,  which  was 
directed  toward  the  sun,  may  have  been  of  this  nature. 

The  influence  of  the  ethereal  medium  on  the  motions 
of  Halley's  comet,  will  be  known  after  another  revolu- 
tion, and  future  astronomers  will  learn,  by  the  accuracy 
of  its  returns,  whether  it  has  met  with  any  unknown 
cause  of  disturbance  in  its  distant  journey.  Undiscovered 
planets,  beyond  the  visible  boundary  of  our  system,  may 
change  its  path  and  the  period  of  its  revolution,  and  thus 
may  indirectly  reveal  to  us  their  existence,  and  even 
their  physical  nature  and  orbit.  The  secrets  of  the  yet 
more  distant  heavens  may  be  disclosed  to  future  genera- 
tions by  comets  which  penetrate  still  farther  into  space, 
such  as  that  of  1763,  which,  if  any  faith  may  be  placed 
in  the  computation,  goes  nearly  forty-three  times  farther 
from  the  sun  than  Halley's  does,  and  shows  that  the 
sun's  attraction  is  powerful  enough,  at  the  enormous 
distance  of  15,500  millions  of  miles,  to  recall  the  comet 
to  its  perihelion.  The  periods  of  some  comets  are  said 
to  be  of  many  thousand  years,  and  even  the  average  time 
of  the  revolution  of  comets  generally  is  about  a  thousand 
years  ;  which  proves  that  the  sun's  gravitating  force  ex- 
tends very  far.  La  Place  estimates  that  the  solar  at- 
traction is  felt  throughout  a  sphere  whose  radius  is  a 
hundred  millions  of  times  greater  than  the  distance  of 
the  earth  from  the  sun. 

Authentic  records  of  Halley's  comet  do  not  extend  be- 
yond the  year  1456,  yet  it  may  be  traced,  with  some 
degree  of  probability,  even  to  a  period  preceding  the 
Christian  em.  But  as  the  evidence  only  rests  upon 
coincidences  of  its  periodic  time,  which  may  vary  as 
much  as  eighteen  months  from  the  disturbing  action  of 
the  planets,  its  identity  with  comets  of  such  remote 
times  must  be  regarded  as  extremely  doubtful. 

This  is  the  first  comet  whose  periodicity  has  been 
established.  It  is  also  the  first  whose  elements  have 
been  determined  from  observations  made  in  Europe  ;  for 
although  the  comets  which  appeared  in  the  years  240, 
539,  565,  and  837,  are  the  most  ancient  of  those  whose 


SECT.  XXXVI.  ENCKE'S  COMET.  345 

orbits  have  been  traced,  their  elements  were  computed 
from  Chinese  observations. 

Besides  Halley's  and  Lexel's  comets,  two  others  are 
now  proved  to  form  part  of  our  system ;  that  is  to  say, 
they  return  to  the  sun  at  intervals,  one  of  three  years, 
and  the  other  of  6J  years  nearly.  The  first,  generally 
called  Encke's  comet,  or  the  comet  of  the  short  period, 
was  first  seen  by  MM.  Messier  and  Mechain,  in  1786, 
again  by  Miss  Herschel  hi  1805,  and  its  returns,  in  the 
years  1805  and  1819,  were  observed  by  other  astrono- 
mers, under  the  impression  that  all  four  were  different 
bodies.  However,  Professor  Encke  not  only  proved 
their  identity,  but  determined  the  circumstances  of  the 
comet's  motion.  Its  reappearance  in  the  years  1825, 
1828,  and  1832,  accorded  with  the  orbit  assigned  by  M. 
Encke,  who  thus  established  the  length  of  its  period  to 
be  1204  days,  nearly.  This  comet  is  very  small,  of 
feeble  light,  and  invisible  to  the  naked  eye,  except 
under  very  favorable  circumstances,  and  in  particular 
positions.  It  has  no  tail,  it  revolves  in  an  ellipse  of 
great  eccentricity  inclined  at  an  angle  of  13°  22'  to  the 
plane  of  the  ecliptic,  and  is  subject  to  considerable  per- 
turbations from  the  attraction  of  the  planets,  which 
occasion  variations  in  its  periodic  time.  Among  the 
many  perturbations  to  which  the  planets  are  liable, 
their  mean  motions,  and  therefore  the  major  axes  of 
their  orbits,  experience  no  change  ;  while  on  the  con- 
trary, the  mean  motion  of  the  moon  is  accelerated  from 
age  to  age — a  circumstance  at  first  attributed  to  the  re- 
sistance of  an  ethereal  medium  pervading  space,  but 
subsequently  proved  to  arise  from  the  secular  diminution 
of  the  eccentricity  of  the  terrestrial  orbit.  Although 
the  resistance  of  such  a  medium  has  not  hitherto  been 
perceived  in  the  motions  of  such  dense  bodies  as  the 
planets  and  satellites,  its  effects  on  the  revolutions  of 
the  two  small  periodic  comets  hardly  leave  a  doubt  of 
its  existence.  From  the  numerous  observations  that 
have  been  made  on  each  return  of  the  comet  of  the 
short  period,  the  elements  have  been  computed  with 
great  accuracy  on  the  hypothesis  of  its  moving  in  vacua. 
Its  perturbations  occasioned  by  the  disturbing  action  of 
the  planets  have  been  determined ;  and  after  everything 


346  ENCKE'S  COMET.       SECT.  XXXVL 

that  could  influence  its  motion  had  been  duly  considered, 
M.  Encke  found  that  an  acceleration  of  about  two  days 
in  each  revolution  has  taken  place  in  its  mean  motion, 
precisely  similar  to  that  which  would  be  occasioned  by 
the  resistance  of  an  ethereal  medium.  And  as  it  cannot 
be  attributed  to  a  cause  like  that  which  produces  the 
acceleration  of  the  moon,  it  must  be  concluded  that  the 
celestial  bodies  do  not  perform  their  evolutions  in  an 
absolute  void,  and  that  although  the  medium  be  too  rare 
to  have  a  sensible  effect  on  the  masses  of  the  planets 
and  satellites,  it  nevertheless  has  a  considerable  influ- 
ence on  so  rare  a  body  as  a  comet.  Contradictory  as  it 
may  seem,  that  the  motion  of  a  body  should  be  accele- 
rated by  the  resistance  of  an  ethereal  medium,  the 
truth  becomes  evident  if  it  be  considered  that  both 
planets  and  comets  are  retained  in  their  orbits  by  two 
forces  which  exactly  balance  one  another ;  namely,  the 
centrifugal  force  producing  the  velocity  in  the  tangent, 
and  the  attraction  of  the  gravitating  force  directed  to 
the  center  of  the  sun.  If  one  of  these  forces  be  dimin- 
ished by  any  cause,  the  other  will  be  proportionally 
increased.  Now,  the  necessaiy  effect  of  a  resisting 
medium  is  to  diminish  the  tangential  velocity,  so  that 
the  balance  is  destroyed,  gravity  preponderates,  the 
body  descends  toward  the  sun  till  equilibrium  is  again 
restored  between  the  two  forces;  and  as  it  then  de- 
scribes a  smaller  orbit  it  moves  with  increased  velocity. 
Thus,  the  resistance  of  an  ethereal  medium  actually 
accelerates  the  motion  of  a  body ;  but  as  the  resisting 
force  is  confined  to  the  plane  of  the  orbit,  it  has  no  in- 
fluence whatever  on  the  inclination  of  the  orbit,  or  on 
the  place  of  the  nodes.  In  computing  its  effect,  M. 
Encke  assumed  the  increase  to  be  inversely  as  the 
squares  of  the  distances,  and  that  its  resistance  acts  as  a 
tangential  force  proportional  to  the  squares  of  the 
comet's  actual  velocity  in  each  point  of  its  orbit.  The 
other  comet  belonging  to  our  system,  which  returns  to 
its  perihelion  after  a  period  of  6|  years,  has  been  ac- 
celerated in  its  motion  by  a  whole  day  during  its  last 
revolution,  which  puts  the  existence  of  ether  nearly 
beyond  a  doubt,  and  forms  a  strong  presumption  in  cor- 
roboration  of  the  undulatory  theory  of  light.  Since  this 


SECT.  XXXVI.    BIELA*S  OR  GAMBARTS  COMET.  347 

comet,  which  revolves  nearly  between  the  orbits  of  fhe 
earth  and  Jupiter,  is  only  accelerated  one  day  at  each 
revolution,  while  Encke's,  revolving  nearly  between  the 
orbits  of  Mercury  and  Pallas,  is  accelerated  two,  the 
ethereal  medium  must  increase  in  density  toward  the 
sun.  The  comet  in  question  was  discovered  by  M. 
Biela  at  Johannisberg  on  the  27th  of  February,  1826, 
and  ten  days  afterward  it  was  seen  by  M.  Gambart  at 
Marseilles,  who  computed  its  parabolic  elements,  and 
found  that  they  agreed  with  those  of  the  comets  which 
had  appeared  in  the  years  1789  and  1795,  whence  he 
concluded  them  to  be  the  same  body  moving  in  an 
ellipse,  and  accomplishing  its  revolution  in  2460  days. 
The  perturbations  of  this  comet  were  computed  by  M. 
Damoiseau,  who  predicted  that  it  would  cross  the  plane 
of  the  ecliptic  on  the  29th  of  October,  1832,  a  little 
before  midnight,  at  a  point  nearly  18,484  miles  within 
the  earth's  orbit;  and  as  M.  Olbers  of  Bremen,  in  1805, 
had  determined  the  radius  of  the  comet's  head  to  be 
about  21,136  miles,  it  was  evident  that  its  nebulosity 
would  envelop  a  portion  of  the  earth's  orbit,  a  circum- 
stance which  caused  some  alarm  in  France,  from  the 
notion  that  if  any  disturbing  cause  had  delayed  the 
arrival  of  the  comet  for  one  month,  the  earth  must  have 
passed  through  its  head.  M.  Arago  dispelled  these 
fears  by  his  excellent  treatise  on  comets  in  the  An- 
nuaire  of  1832,  where  he  proves,  that  as  the  earth 
would  never  be  nearer  the  comet  than  18,000,000 
British  leagues,  there  could  be  no  danger  of  collision. 
The  earth  is  in  more  danger  from  these  two  small 
comets  than  from  any  other.  Encke's  crosses  the  ter- 
restrial orbit  sixty  times  in  a  century,  and  may  ulti- 
mately come  into  collision:  but  both  are  so  extremely 
rare,  that  little  injury  is  to  be  apprehended. 

The  earth  would  fall  to  the  sun  in  64i  days,  if  it 
were  struck  by  a  comet  with  sufficient  impetus  to  de- 
stroy its  centrifugal  force.  What  the  earth's  primitive 
velocity  may  have  been,  it  is  impossible  to  say.  There- 
fore a  comet  may  have  given  it  a  shock  without  changing 
the  axis  of  rotation,  but  only  destroying  part  of  its  tan- 
gential velocity,  so  as  to  diminish  the  size  of  the  orbit — a 
thing  by  no  means  impossible,  though  highly  improbable. 


348  THE  SHOCK  OP  A  COMET.         SECT.  XXXVI. 

At  all  events,  there  is  no  proof  of  this  having  occurred; 
and  it  is  manifest  that  the  axis  of  the  earth's  rotation 
has  not  been  changed,  because,  as  the  ether  offers  no 
sensible  resistance  to  so  dense  a  body  as  the  earth,  the 
libration  would  to  this  day  be  evident  in  the  variation  it 
must  have  occasioned  in  the  terrestrial  latitudes.  Sup- 
posing the  nucleus  of  a  comet  to  have  a  diameter  only 
equal  to  the  fourth  part  of  that  of  the  earth,  and  that  its 
perihelion  is  nearer  to  the  sun  than  we  are  ourselves,  its 
orbit  being  otherwise  unknown,  M.  Arago  has  computed 
that  the  probability  of  the  earth  receiving  a  shock  from 
it  is  only  one  in  281  millions,  and  that  the  chance  of  our 
coming  in  contact  with  its  nebulosity  is  about  ten  or 
twelve  times  greater.  Only  comets  with  retrogade  mo- 
tions can  come  into  direct  collision  with  the  earth,  and  if 
the  momentum  were  great  the  event  might  be  fatal; 
but  in  general  the  substance  of  comets  is  so  rare,  that  it 
is  likely  they  would  not  do  much  harm  if  they  were  to 
impinge  ;  and  even  then  the  mischief  would  probably  be 
local,  and  the  equilibrium  soon  restored,  provided  the 
nucleus  were  gaseous,  or  very  small.  It  is,  however, 
more  probable  that  the  earth  would  only  be  deflected  a 
little  from  its  course  by  the  approach  of  a  comet,  with- 
out being  touched  by  it.  The  comets  that  have  come 
nearest  to  the  earth  were  that  of  the  year  837,  which 
remained  four  days  within  less  than  1,240,000  leagues 
from  our  orbit;  that  of  1770,  which  approached  within 
about  six  times  the  distance  of  the  moon.  The  cele- 
brated comet  of  1680  also  came  very  near  to  us ;  and 
the  comet  whose  period  is  61  years  was  ten  times  nearer 
the  earth  in  1805  than  in  1832,  when  it  caused  so  much 
alarm. 

Encke's  and  Biela's  comets  are  at  present  far  removed 
from  the  influence  of  Jupiter,  but  they  will  not  always 
remain  so,  because  the  aphelia  and  nodes  of  the  orbits 
of  these  two  comets  being  the  points  which  approach 
nearest  to  the  orbit  of  Jupiter,  at  each  meeting  of  the 
planet  and  comets  which  shall  take  place  there,  the 
major  axi-s  of  Encke's  comet  will  be  increased,  and  that 
of  Biela's  diminished,  till  in  the  course  of  time,  when 
the  proximity  has  increased  sufficiently,  the  orbits  will 
be  completely  changed,  as  that  of  Lexel's  was  in  1770, 


SKCT.  XXXVI.     ENCKE'S  AND  BIELA'S  COMETS.  349 

Every  twenty-third  year,  or  after  seven  revolutions  of 
Encke's  cornet,  its  greatest  proximity  to  Jupiter  takes 
place,  and  at  that  lime  his  attraction  increases  the  pe- 
riod of  its  revolution  by  nine  days — a  circumstance 
which  took  place  in  the  end  of  the  years  1820  and  1843. 
But  from  the  position  of  the  bodies  there  is  a  diminution 
of  three  days  in  the  six  following  revolutions,  which 
reduces  the  increase  to  six  days  in  seven  revolutions. 
Thus  before  the  year  1819,  the  periodic  time  of  Encke's 
comei;  was  1204  days,  and  it  was  1219  days  in  accom- 
plishing its  last  revolution,  which  terminated  in  1845. 
By  this  progressive  increase  the  orbit  of  the  comet  will 
reach  that  of  Jupiter  in  seven  or  eight  centuries,  and 
then  by  the  very  near  approach  of  the  two  bodies  it  wiH 
be  completely  changed. 

At  present  the  earth  and  Mercury  have  the  most 
powerful  influence  on  the  motions  of  Encke's  and  Biela's 
comets  ;  and  have  had  for  so  long  a  time  that,  according 
to  the  computation  of  Mr.  Airy,  the  present  orbit  of  the 
latter  was  formed  by  the  attraction  of  the  earth,  and 
that  of  Encke's  by  the  action  of  Mercury.  With  re- 
gard to  the  latter  comet,  that  event  must  have  taken 
place  in  February,  1776.  Tn  1786  Encke's  comet  had 
both  a  tail  and  a  nucleus,  now  it  has  neither  ;  a  singular 
instance  of  the  possibility  of  their  disappearance. 

Comets  in  or  near  their  perihelion  move  with  pro- 
digious velocity.  That  of  1680  appears  to  have  gone 
half  round  the  sun  in  ten  hours  and  a  half,  moving  at 
the  rate  of  880,000  miles  an  hour.  If  its  enormous 
centrifugal  force  had  ceased  when  passing  its  perihe- 
lion, it  would  have  fallen  to  the  sun  in  about  three 
minutes,  as  it  was  then  less  than  147,000  miles  from  his 
surface.  So  near  the  sun,  it  would  be  exposed  to  a  heat 
27,500  times  greater  than  that  received  by  the  earth ; 
and  as  the  sun's  heat  is  supposed  to  be  in  proportion  to 
the  intensity  of  his  light,  it  is  probable  that  a  degree  of 
heat  so  intense  would  be  sufficient  to  convert  into  vapor 
every  terrestrial  substance  with  which  we  are  acquainted. 
At  the  perihelion  distance  the  sun's  diameter  would  be 
seen  from  the  comet  under  an  angle  of  73°,  so  that  the 
sun,  viewed  from  the  comet,  would  nearly  cover  the 
whole  extent  of  the  heavens  from  the  horizon  to  tho 
GG 


350  FALL  OF  COMETS  TO  THE  SUN.    SECT.  XXXVI. 

zenith.  As  this  comet  is  presumed  to  have  a  period  of 
575  years,  the  major  axis  of  its  orbit  must  be  so  great, 
that  at  the  aphelion  the  sun's  diameter  would  only  sub- 
tend an  angle  of  about  fourteen  seconds,  which  is  not 
so  great  by  half  as  the  diameter  of  Mars  appears  to  us 
when  in  opposition.  The  sun  would  consequently  im- 
part  no  heat,  so  that  the  comet  would  then  be  exposed 
to  the  temperature  of  the  ethereal  regions,  which  is  58° 
below  the  zero  point  of  Fahrenheit.  A  body  of  such 
tenuity  as  the  comet,  moving  with  such  velocity,  must 
have  met  with  great  resistance  from  the  dense  atmos- 
phere of  the  sun,  while  passing  so  near  his  surface  at 
its  perihelion.  The  centrifugal  force  must  consequently 
have  been  diminished,  and  the  sun's  attraction  propor- 
tionally augmented,  so  that  it  must  have  come  nearer  to 
the  sun  in  1680  than  in  its  preceding  revolution,  and 
would  subsequently  describe  a  smaller  orbit.  As  this 
diminution  of  its  orbit  will  be  repeated  at  each  revolu- 
tion, the  comet  will  infallibly  end  by  falling  on  the  sur- 
face of  the  sun,  unless  its  course  be  changed  by  the  dis- 
turbing influence  of  some  large  body  in  the  unknown 
expanse  of  creation.  Our  ignorance  of  the  actual  den- 
sity of  the  sun's  atmosphere,  of  the  density  of  the 
comet,  and  of  the  period  of  its  revolution,  renders  it 
impossible  to  form  any  idea  of  the  number  of  centuries 
which  must  elapse  before  this  event  takes  place. 

The  same  cause  may  affect  the  motions  of  the  planets, 
and  ultimately  be  the  means  of  destroying  the  solar  sys- 
tem. But,  as  Sir  John  Herschel  observes,  they  could 
hardly  all  revolve  in  the  same  direction  round  the  sun 
for  so  many  ages  without  impressing  a  corresponding 
motion  on  the  ethereal  fluid,  which  may  preserve  them 
from  the  accumulated  effects  of  its  resistance.  Should 
this  material  fluid  revolve  about  the  sun  like  a  vortex,  it 
will  accelerate  the  revolutions  of  such  comets  as  have 
direct  motions,  and  retard  those  that  have  retrograde 
motions. 

The  comet  which  appeared  unexpectedly  in  the  be- 
ginning of  the  year  ]843,  was  on-e  of  the  most  splendid 
that  ever  visited  the  solar  system.  It  was  in  the  con- 
stellation of  Antinous  in  the  end  of  January,  at  a  dis- 
tance of  115  millions  of  miles  from  the  earth,  and  it 


S«CT.  XXXVI.  COMET  OF  1843.  351 

passed  through  its  perihelion  on  the  27th  of  February, 
when  it  was  lost  in  the  sun's  rays ;  but  it  began  to  be 
visible  about  the  3d  of  March,  at  which  time  it  was  near 
the  star  Iota  Cetae,  and  its  tail  extended  toward  the 
Hare.  The  brightness  of  the  comet  and  the  length  of 
its  tail  continued  to  increase  till  the  latter  stretched  far 
beyond  the  constellation  of  the  Hare  toward  a  point 
above  Sirius.  Stars  were  distinctly  seen  through  it, 
and  when  near  perihelion  the  comet  was  so  bright  that 
it  was  seen  in  clear  sunshine  in  the  United  States 
like  a  white  cloud.  The  motion  was  retrograde,  and 
on  leaving  the  solar  system  it  retreated  so  rapidly  at 
once  from  the  sun  and  earth  that  it  was  soon  lost  sight 
of  for  want  of  light.  On  the  1st  of  April  it  was  between 
the  sun  and  the  earth,  and  only  40  millions  of  miles  from 
the  latter ;  and  as  its  tail  was  at  least  60  millions  of 
miles  long,  and  20  millions  of  miles  broad,  we  probably 
passed  through  it  without  being  aware  of  it.  There  is 
some  discrepancy  in  the  different  computations  of  the 
elements  of  the  orbit,  but  in  the  greater  number  of 
cases  the  perihelion  distance  was  found  to  be  less  than 
the  semidiameter  of  the  sun,  so  that  the  comet  must 
have  grazed  his  surface,  if  it  did  not  actually  impinge 
obliquely  on  him. 

The  perihelion  distance  of  this  comet  differs  little 
from  that  of  the  great  comet  of  1668,  which  came  so 
near  the  sun.  The  motion  of  both  was  retrograde,  and 
a  certain  resemblance  in  the  two  orbits  makes  it  proba- 
ble that  they  are  the  same  body  performing  a  revolution 
in  175  years. 

Though  already  so  well  acquainted  with  the  motions 
of  comets,  we  know  nothing  of  then*  physical  constitu- 
tion. A  vast  number,  especially  of  telescopic  comets, 
are  only  like  clouds  or  masses  of  vapor,  often  without 
tails.  Such  were  the  comets  which  appeared  in  the 
years  1795,  1797,  and  1798.  But  the  head  commonly 
consists  of  a  concentrated  mass  of  light,  like  a  planet, 
surrounded  by  a  very  transparent  atmosphere,  and  the 
whole,  viewed  with  a  telescope,  is  so  diaphanous,  that 
the  smallest  star  may  be  seen  even  through  the  densest 
part  of  the  nucleus  ;  in  general  their  solid  parts,  if  they 
have  any,  are  so  minute,  that  they  have  no  sensible 


352  MASSES  OF  COMETS.  SECT.  XXXVI. 

diameter,  like  that  of  the  comet  of  1811,  which  ap- 
peared to  Sir  William  Herschel  like  a  luminous  point 
in  the  middle  of  the  nebulous  matter.  The  nuclei, 
which  seemed  to  be  formed  of  the  denser  strata  of  that 
nebulous  matter  in  successive  coatings,  are  sometimes 
of  great  magnitude.  Those  comets  which  came  to  the 
sun  in  the  years  1799  and  1807,  had  nuclei  whose  di- 
ameters measured  180  and  275  leagues  respectively, 
and  the  second  comet  of  1811  had  a  nucleus  of  1350 
leagues  in  diameter. 

It  must  however  be  stated,  that  as  comets  are  gene- 
rally at  prodigious  distances  from  the  earth,  the  solid 
parts  of  the  nuclei  appear  like  mere  points  of  light,  so 
minute  that  it  impossible  to  measure  them  with  any 
kind  of  accuracy,  so  that  the  best  astronomers  often 
differ  in  the  estimation  of  their  size,  by  one-half  of  the 
whole  diameter.  The  transit  of  a  comet  across  the  sun 
would  afford  the  best  information  with  regard  to  the 
nature  of  the  nuclei.  It  was  computed  that  such  an 
event  was  to  take  place  in  the  year  1827  ;  unfortunately 
the  sun  was  hid  by  clouds  from  the  British  astronomers, 
but  it  was  examined  at  Viviers  and  at  Marseilles  at  the 
time  the  comet  must  have  been  projected  on  its  disc, 
but  no  spot  or  cloud  was  to  be  seen,  so  that  it  must 
have  had  no  solid  part  whatever.  The  nuclei  of  many 
comets  which  seemed  solid  and  brilliant  to  the  naked 
eye  have  been  resolved  into  mere  vapor  by  telescopes 
of  high  powers ;  in  Halley's  comet  there  was  no  solid 
part  at  all. 

The  nebulosity  immediately  round  the  nucleus  is  so 
diaphanous  that  it  gives  little  light ;  but  at  a  small  dis- 
tance the  nebulous  matter  becomes  suddenly  brilliant, 
so  as  to  look  like  a  bright  ring  round  the  body. 
Sometimes  there  are  two  or  three  of  these  luminous 
concentric  rings  separated  by  dark  intervals,  but  they 
are  generally  incomplete  on  the  part  next  the  tail. 

These  annular  appearances  are  an  optical  effect, 
arising  from  a  succession  of  envelops  of  the  nebulous 
matter  with  intervals  between  them,  of  which  the  first 
is  sometimes  in  contact  with  the  nucleus  and  sometimes 
not.  The  thickness  of  these  bright  diaphanous  coatings 
in  the  comets  of  1799  and  1807  were  about  7000  and 


SECT.  XXXVI.  ENVELOPS  OF  COMETS.  353 

10,000  leagues  respectively ;  and  in  the  first  comet  of 
1611,  the  luminous  ring  was  8000  leagues  thick,  and 
the  distance  between  its  interior  surface  and  the  center 
of  the  head  was  10,000  leagues.  The  latter  comet  was 
by  much  the  most  brilliant  that  has  been  seen  in  mod- 
ern times ;  it  was  first  discovered  in  this  country  by  Mr. 
James  Vietch  of  Inchbonny,  and  was  observed  in  all  its 
changes  by  Sir  William  Herschel  and  M.  Olbers.  To 
the  naked  eye,  the  head  had  the  appearance  of  an  ill- 
defined  round  mass  of  light,  which  was  resolved  hi  to 
several  distinct  parts  when  viewed  with  a  telescope. 
A  very  brilliant  interior  circular  mass  of  nebulous  mat- 
ter was  surrounded  by  a  black  space  having  a  parabolic 
form,  veiy  distinct  from  the  dark  blue  of  the  sky.  This 
dark  space  was  of  a  very  appreciable  breadth.  Exterior 
to  the  black  interval  there  was  a  luminous  parabolic 
contour  of  considerable  thickness,  which  was  prolonged 
on  each  side  in  two  diverging  branches,  which  formed 
the  bifid  tail  of  the  comet.  Sir  William  Herschel  found 
that  the  brilliant  interior  circular  mass  lost  the  distinct- 
ness of  its  outline  as  he  increased  the  magnifying  power 
of  the  telescope,  and  presented  the  appearance  of  a 
more  and  more  diffuse  mass  of  greenish  or  bluish-green 
light,  whose  intensity  decreased  gradually,  not  from  the 
center,  but  from  an  eccentric  brilliant  speck,  supposed 
to  be  the  trtfly  solid  part  of  the  comet.  The  luminous 
envelop  was  of  a  decided  yellow,  which  contrasted 
strongly  with  the  greenish  tint  of  the  interior  nebulous 
mass.  Stars  were  nearly  veiled  by  the  luminous  en- 
velop, while,  on  the  contrary,  Sir  William  Herschel  saw 
three  extremely  small  stars  shining  clearly  in  the  black 
space,  which  was  singularly  transparent.  As  the  en- 
velop* were  formed  in  succession  as  the  comet  ap- 
proached the  sun,  Sir  William  Herschel  conceived  them 
to  be  vapors  raised  by  his  heat  at  the  surface  of  the 
nucleus,  and  suspended  round  it  like  a  vault  or  dome  by 
the  elastic  force  of  an  extensive  and  highly  transparent 
atmosphere.  In  coming  to  the  sun,  the  coatings  began 
to  form  when  the  comet  was  as  distant  as  the  orbit  of 
Jupiter,  and  in  its  return  they  very  soon  entirely  van- 
ished ;  but  a  new  one  was  formed  after  it  had  retreated 
as  far  as  the  orbit  of  Mars,  which  lasted  for  a  few  days. 
23  GG2 


354  TAILS  OF  COMETS.  SECT.  XXXVI. 

Indeed,  comets  in  general  are  subject  to  sudden  and 
violent  convulsions  in  their  interior,  even  when  far  from 
the  sun,  which  produce  changes  that  are  visible  at  enor- 
mous distances,  and  baffle  all  attempts  at  explanation, — 
probably  arising  from  electricity,  or  even  causes  with 
which  we  are  unacquainted.  The  envelops  surrounding 
the  nucleus  of  the  comet  on  the  side  next  to  the  sun, 
diverge  on  the  opposite  side,  where  they  are  prolonged 
into  the  form  of  a  hollow  cone,  which  is  the  tail.  Two 
repulsive  forces  seem  to  be  concerned  in  producing 
this  effect ;  one  from  the"  comet  and  another  from  the 
sun,  the  latter  being  the  most  powerful.  The  envelops 
are  nearer  the  center  of  the  comet  on  the  side  next  to 
the  sun,  where  these  forces  are  opposed  to  one  an- 
other; but  on  the  other  side  the  forces  conspire  to 
form  the  tail,  conveying  the  nebulous  particles  to  enor- 
mous distances. 

"•  The  lateral  edges  of  the  tail  reflect  more  light  than 
the  central  part,  because  the  line  of  vision  passes  through 
a  greater  depth  of  nebulous  matter,  which  produces  the 
effect  of  two  streams  somewhat  like  the  aurora.  Stars 
shine  with  undiminished  lustre  through  the  central  part 
of  the  tail,  because  their  rays  traverse  it  perpendicularly 
to  its  thickness ;  but  though  distinctly  seen  through  its 
edges,  their  light  is  weakened  by  its  oblique  transmis- 
sion. The  tail  of  the  great  comet  of  1811  was  of  won- 
derful tenuity ;  stars  which  would  have  been  entirely 
concealed  by  the  slightest  fog,  were  seen  through  64,000 
leagues  of  nebulous  matter  without  the  smallest  refrac- 
tion. Possibly  some  part  of  the  changes  in  the  appear- 
ance of  the  tails  arises  from  rotation.  Several  comets 
have  been  observed  to  rotate  about  an  axis  passing 
through  the  center  of  the  tail.  That  of  1825  performed 
its  rotation  in  20£  hours,  and  the  rapid  changes  in  the 
luminous  sectors  which  issued  from  the  nucleus  of  Hal- 
ley's  comet,  in  all  probability  were  owing  to  rotatory 
motion. 

The  two  streams  of  light  which  form  the  edges  of  the 
tail,  in  most  cases  unite  at  a  greater  or  less  distance  from 
the  nucleus,  and  are  generally  situate  in  the  plane  of 
the  orbit.  The  tails  follow  comets  in  their  descent 
toward  the  sun,  but  precede  them  in  their  return,  with 


S*cr.  XXXVI.  TAILS  OF  COMETS.  365 

a  small  degree  of  curvature ;  their  apparent  extent  and 
form  vary  according  to  the  positions  of  the  orbits  with 
regard  to  the  ecliptic.  In  some  cases,  the  tail  has  been 
at  right  angles  to  the  line  joining  the  sun  and  comet. 
The  curvature  is  in  part  owing  to  the  resistance  of  the 
ether»  and  partly  to  the  velocity  of  the  comet  being 
greater  than  that  of  the  particles  at  the  extremity  of  its 
tail,  which  lag  behind.  The  tails  are  generally  of  enor- 
mous lengths  ;  the  comet  of  1811  had  one  no  less  than  a 
hundred  millions  of  miles  in  length,  and  those  which 
appeared  in  the  years  1618,  1680,  and  1769,  had  tails 
which  extended  respectively  over  104,  90,  and  97  de- 
grees of  space.  Consequently,  when,  the  heads  of  these 
comets  were  set,  a  portion  of  the  extremity  of  their  tails 
was  still  in  the  zenith.  Sometimes  the  tail  is  divided 
into  several  branches,  like  the  comet  of  1744,  which  had 
six,  separated  by  dark  intervals,  each  of  them  about  4° 
broad,  and  from  30°  to  44°  long.  They  were  probably 
formed  by  three  hollow  cones  of  the  nebulous  matter 
proceeding  from  the  different  envelops,  and  inclosing  one 
another  with  intervals  between ;  the  lateral  edges  of 
these  cones  would  give  the  appearance  of  six  streams  of 
light.  The  tails  do  not  attain  their  full  magnitude  till 
the  comet  has  left  the  sun.  When  comets  first  appear, 
they  resemble  round  films  of  vapor  with  little  or  no  tail. 
As  they  approach  the  sun,  they  increase  in  brilliancy, 
and  their  tail  in  length,  till  they  are  lost  in  his  rays  ;  and 
it  is  not  till  they  emerge  from  the  sun's  more  vivid  light 
that  they  assume  their  full  splendor.  They  then  grad- 
ually decrease,  their  tails  diminish,  and  they  disappear 
nearly  or  altogether  before  they  are  beyond  the  sphere 
of  telescopic  vision.  Many  comets  have  no  tails,  as  for 
example  Encke's  comet,  and  that  discovered  by  M.  Biela, 
both  of  which  are  small  and  insignificant  objects.  The 
comets  which  appeared  in  the  years  1585,  1763,  and 
1682,  were  also  without  tails,  though  the  latter  is  re- 
corded to  have  been  as  bright  as  Jupiter.  The  matter 
of  the  tail  must  be  extremely  buoyant  to  precede  a  body 
moving  with  such  velocity ;  indeed  the  rapidity  of  its 
ascent  cannot  be  accounted  for.  It  has  been  attributed 
to  that  power  in  the  sun  which  produces  those  vibrations 
of  ether  which  constitute  light :  but  as  this  theory  will 


356  TAILS  OF  COMETS.  SECT.  XXXVI. 

not  account  for  the  comet  of  1824,  which  is  said  to  have 
had  two  tails,  one  directed  toward  the  sun,  and  a  very 
short  one  diametrically  opposite  to  it,  pur  ignorance  on 
this  subject  must  be  confessed.  In  this  case  the  repel- 
ling power  of  the  comet  seems  to  have  been  greater  than 
that  of  the  sun.  Whatever  that  unknown  power  may 
be,  there  are  instances  in  which  its  effects  are  enormous, 
for  immediately  after  the  great  comet  of  1680  had  passed 
its  perihelion,  its  tail  was  100,000,000  miles  in  length, 
and  was  projected  from  the  comet's  head  in  the  short 
space  of  two  days.  A  body  of  such  extreme  tenuity  as 
a  comet  is  most  likely  incapable  of  an  attraction  power- 
ful enough  to  recall  matter  sent  to  such  an  enormous 
distance  ;  it  is  therefore  in  all  probability  scattered  in 
space,  which  may  account  for  the  rapid  decrease  ob- 
served in  the  tails  of  comets  every  time  they  return  to 
their  perihelia.  Should  the  great  comet  of  1843  prove 
to  be  the  same  with  that  of  1668,  its  tail  must  have  di- 
minished considerably. 

It.  is  remarkable  that  although  the  tails  of  comets  in- 
crease in  length  as  they  approach  their  perihelia,  there 
is  reason  to  believe  that  the  real  diameter  of  the  head 
contracts  on  coming  near  the  sun,  and  expands  rapidly 
on  leaving  him.  Hevelius  first  observed  this  phenome- 
non, which  Encke's  comet  has  exhibited  in  a  very  ex- 
traordinary degree.  On  the  28th  of  October,  1828,  this 
comet  was  about  three  times  as  far  from  the  sun  as  it 
was  on  the  24th  of  December,  yet  at  the  first  date  its 
apparent  diameter  was  twenty-five  times  greater  than  at 
the  second,  the  decrease  being  progressive.  M.  Valz 
attributes  the  circumstance  to  a  real  condensation  of  vol- 
ume from  the  pressure  of  the  ethereal  medium,  which 
increases  most  rapidly  in  density  toward  the  surface  of 
the  sun,  and  forms  an  extensive  atmosphere  around  him. 
It  did  not  occur  to  M.  Valz,  however,  that  the  ethereal 
fluid  would  penetrate  the  nebulous  matter  instead  of 
compressing  it.  Sir  John  Herschel,  on  the  contrary, 
conjectures  that  it  may  be  owing  to  the  alternate  con- 
version of  evaporable  materials  in  the  upper  regions  of 
the  transparent  atmosphere  of  comets  into  the  states  of 
visible  cloud  and  invisible  gas  by  the  effects  of  heat  and 
cold  ;  or  that  some  of  the  external  nebulous  envelops 


SKCT.  XXXVI.  LIGHT  OF  COMETS.  357 

may  come  into  view  when  the  comet  arrives  at  a  darker 
part  of  the  sky,  which  were  overpowered  by  the  supe- 
rior light  of  the  sun  while  in  his  vicinity.  The  first  of 
these  hypotheses  he  considers  to  be  perfectly  confirmed 
by  his  observations  on  Halley's  comet,  made  at  the  Cape 
of  Good  Hope,  after  its  return  from  the  sun.  He  thinks 
that  in  all  probability  the  whole  comet,  except  the  dens- 
est part  of  its  nucleus,  vanished  and  was  reduced  to  a 
transparent  and  invisible  state  during  its  passage  at  its 
perihelion,  for  when  it  first  came  into  view  after  leaving 
the  sun  it  had  no  tail,  and  its  aspect  was  completely 
changed.  A  parabolic  envelop  soon  began  to  appear, 
and  increased  so  much  and  so  rapidly  that  its  augmenta- 
tion was  visible  to  the  eye.  This  increase  continued  till 
it  became  so  large  and  so  faint,  that  at  last  it  vanished 
entirely,  leaving  only  the  nucleus  and  a  tail,  which  it  had 
again  acquired,  but  which  also  vanished,  so  that  at  last 
the  nucleus  alone  remained.  Not  only  the  tails,  but  the 
nebulous  part  of  comets  diminishes  every  time  they  re- 
turn to  their  perihelia ;  after  frequent  returns  they  ought 
to  lose  it  altogether,  and  present  the  appearance  of  a 
fixed  nucleus  :  this  ought  to  happen  sooner  to  comets  of 
short  periods.  M.  de  la  Place  supposes  that  the  comet  of 
1682  must  be  approaching  rapidly  to  that  state.  Should 
the  substances  be  altogether,  or  even  to  a  great  degree, 
evaporated,  the  comet  would  disappear  forever.  Possi- 
bly comets  may  have  vanished  from  our  view  sooner  than 
they  would  otherwise  have  done  from  this  cause. 

If  comets  shine  by  borrowed  light,  they  ought,  in 
certain  positions,  to  exhibit  phases  like  the  moon ;  but 
no  such  appearance  has  been  detected  except  in  one 
instance,  when  they  are  said  to  have  been  observed  by 
Hevelius  and  La  Hire  in  the  year  1682.  In  general, 
the  light  of  comets  is  dull — that  of  the  comet  of  1811 
was  only  equal  to  the  tenth  part  of  the  light  of  the  full 
moon — yet  some  have  been  brilliant  enough  to  be  visible 
in  full  daylight,  especially  the  comet  of  1744,  which  was 
seen  without  a  telescope  at  one  o'clock  in  the  afternoon, 
while  the  sun  was  shining.  Hence  it  may  be  inferred 
that,  although  some  comets  maybe  altogether  diaphanous, 
others  seem  to  possess  a  solid  mass  resembling  a  planet. 
But  whether  they  shine  by  their  own  or  by  reflected 


358  LIGHT  OF  COMETS  SECT.  XXXVT. 

light  has  never  been  satisfactorily  made  out  till  now. 
Even  if  the  light  of  a  comet  were  polarized,  it  Would 
not  afford  a  decisive  test,  since  a  body  is  capable  of  re- 
flecting light  though  it  shines  by  its  own.  M.  Arago, 
however,  has  with  great  ingenuity  discovered  a  method 
of  ascertaining  this  point,  independent  both  of  phases 
and  polarization. 

Since  the  rays  of  light  diverge  from  a  luminous  point, 
they  will  be  scattered  over  a  greater  space  as  the  dis- 
tance increases,  so  that  the  intensity  of  the  light  on  a 
screen  two  feet  from  the  object,  is  four  times  less  than 
at  the  distance  of  one  foot ;  three  feet  from  the  object 
it  is  nine  times  less,  and  so  on,  decreasing  in  intensity 
as  the  squares  of  the  distances  increase.  As  a  self- 
luminous  surface  consists  of  an  infinite  number  of  lumi- 
nous points,  it  is  clear  that  the  greater  the  extent  of  sur- 
face, the  more  intense  will  be  the  light;  whence  it  may 
be  concluded  that  the  illuminating  power  of  such  a  sur- 
face is  proportional  to  its  extent,  and  decreases  inversely 
as  the  squares  of  the  distances.  Notwithstanding  this, 
a  self-luminous  surface,  plane  or  curved,  viewed  through 
a  hole  in  a  plate  of  metal,  is  of  the  same  brilliancy  at  all 
possible  distances  as  long  as  it  subtends  a  sensible  angle, 
because,  as  the  distance  increases,  a  greater  portion 
comes  into  view,  and  as  the  augmentation  of  surface  is 
as  the  square  of  the  diameter  of  the  part  seen  through 
the  hole,  it  increases  as  the  squares  of  the  distances. 
Hence,  though  the  number  of  rays  from  any  one  point 
of  the  surface  which  pass  through  the  hole,  decreases 
inversely  as  the  squares  of  the  distances,  yet,  as  the 
extent  of  surface  which  comes  into  view  increases  also 
in  that  ratio,  the  brightness  of  the  object  is  the  same  to 
the  eye  as  long  as  it  has  a  sensible  diameter.  For  ex- 
ample— Uranus  is  about  nineteen  times  farther  from  the 
sun  than  we  are,  so  that  the  sun,  seen  from  that  planet, 
must  appear  like  a  star  with  a  diameter  of  a  hundred 
seconds,  and  must  have  the  same  brilliancy  to  the  inhab- 
itants that  he  would  have  to  us  if  viewed  through  a 
small  circular  hole  having  a  diameter  of  a  hundred  sec- 
onds. For  it  is  obvious  that  light  comes  from  every 
point  of  the  sun's  surface  to  Uranus,  whereas  a  very 
small  portion  of  his  disc  is  visible  through  the  hole  :  so 


SECT.  XXXVI.  NUMBER  OF  COMETS.  359 

that  extent  of  surface  exactly  compensates  distance. 
Since,  then,  the  visibility  of  a  self-luminous  object  does 
not  depend  upon  the  angle  it  subtends  as  long  as  it  is 
of  sensible  magnitude,  if  a  comet  shines  by  its  own  light, 
it  should  retain  its  brilliancy  as  long  as  its  diameter  is  of 
a  sensible  magnitude  ;  and  even  after  it  has  lost  an  ap- 
parent diameter,  it  ought  to  be  visible,  like  the  fixed 
stars,  and  should  only  vanish  in  consequence  of  extreme 
remoteness.  That,  however,  is  far  from  being  the  case 
— comets  gradually  become  dim  as  their  distance  in- 
creases, and  vanish  merely  from  loss  of  light,  while 
they  still  retain  a  sensible  diameter,  which  is  proved  by 
observations  made  the  evening  before  they  disappear. 
It  may  therefore  be  concluded,  that  comets  shine  by 
reflecting  the  sun's  light.  The  most  brilliant  comets 
have  hitherto  ceased  to  be  visible  when  about  five  times 
as  far  from  the  sun  as  we  are.  Most  of  the  comets 
that  have  been  visible  from  the  earth  have  their  peri- 
helia within  the  orbit  of  Mars,  because  they  are  invisible 
when  as  distant  as  the  orbit  of  Saturn  :  on  that  account 
there  is  not  one  on  record  whose  perihelion  is  situate 
beyond  the  orbit  of  Jupiter.  Indeed,  the  comet  of  1756, 
after  its  last  appearance,  remained  five  whole  years 
within  the  ellipse  described  by  Saturn  without  being 
once  seen.  More  than  a  hundred  and  forty  comets 
have  appeared  within  the  earth's  orbit  during  the  last 
century  that  have  not  again  been  seen.  If  a  thousand 
years  be  allowed  as  the  average  period  of  each,  it  may 
be  computed,  by  the  theory  of  probabilities,  that  the 
whole  number  which  range  within  the  earth's  orbit 
must  be  1400 ;  but  Uranus  being  about  nineteen  times 
more  distant,  there  may  be  no  less  than  11,200,000 
comets  that  come  within  the  known  extent  of  our  sys- 
tem. M.  Arago  makes  a  different  estimate :  he  con- 
siders that,  as  thirty  comets  are  known  to  have  their 
perihelion  distance  within  the  orbit  of  Mercury,  if  it  be 
assumed  that  comets  are  uniformly  distributed  in  space, 
the  number  having  their  perihelion  within  the  orbit  of 
Uranus  must  be  to  thirty  as  the  cube  of  the  radius  of 
the  orbit  of  Uranus  to  the  cube  of  the  radius  of  the 
orbit  of  Mercury,  which  makes  the  number  of  comets 
amount  to  3,529,470.  But  that  number  may *  e  doubled, 


360  ORBITS  OF  COMETS.  SECT.  XXXVI. 

if  it  be  considered  that,  in  consequence  of  daylight,  fogs, 
and  great  southern  declination,  one  comet  out  of  two 
must  be  hid  from  us.  According  to  M.  Arago,  more 
than  seven  millions  of  comets  frequent  the  planetary 
orbits. 

The  different  degrees  of  velocity  with  which  the 
planets  and  comets  were  originally  propelled  in  space  is 
the  sole  cause  of  the  diversity  in  the  form  of  their  orbits, 
which  depends  only  upon  the  mutual  relation  between 
the  projectile  force  and  the  sun's  attraction. 

When  the  two  forces  are  exactly  equal  to  one  another, 
circular  motion  is  produced ;  when  the  ratio  of  the  pro- 
jectile to  the  central  force  is  exactly  that  of  1  to  the 
square  root  of  2,  the  motion  is  parabolic ;  any  ratio  be- 
tween these  two  will  cause  a  body  to  move  in  an  ellipse, 
and  any  ratio  greater  than  that  of  1  to  the  square  root  of 
2  will  produce  hyperbolic  motion  (N.  222). 

The  celestial  bodies  might  move  in  any  one  of  these 
four  curves  by  the  law  of  gravitation ;  but  as  one  par- 
ticular velocity  is  necessary  to  produce  either  circular  or 
parabolic  motion,  such  motions  can  hardly  be  supposed  to 
exist  in  the  solar  system,  where  the  bodies  are  liable  to 
such  mutual  disturbances  as  would  infallibly  change  the 
ratio  of  the  forces,  and  cause  them  to  move  in  ellipses 
in  the  first  case,  and  hyperbolas  in  the  other.  On  the 
contrary,  since  every  ratio  between  equality  and  that  of 
1  to  the  square  root  of  2  will  produce  elliptical  motion,  it 
is  found  in  the  solar  system  in  all  its  varieties,  from  that 
which  is  nearly  circular,  to  such  as  borders  on  the  para- 
bolic from  excessive  eUipticity.  On  this  depends  the 
stability  of  the  system  ;  the  mutual  disturbances  only 
cause  the  orbits  to  become  more  or  less  eccentric  with- 
out changing  their  nature. 

For  the  same  reason  the  bodies  of  the  solar  system 
might  have  moved  in  an  infinite  variety  of  hyperbolas, 
since  any  ratio  of  the  forces,  greater  than  that  which 
causes  parabolic  motion,  will  make  a  body  move  in  one 
of  these  curves.  Hyperbolic  motion  is  however  very 
rare  ;  only  two  comets  appear  to  move  in  orbits  of  that 
nature,  those  of  1771  and  1824  ;  probably  all  such  com- 
ets have  already  come  to  their  perihelia,  and  conse- 
quently will  never  return. 


SKCT.  XXXVH.  FIXED  STARS.  361 

The  ratio  of  the  forces  which  fixed  the  nature  of  the 
celestial  orbits  is  thus  easily  explained  ;  but  the  circum- 
stances which  determined  these  ratios,  which  caused 
some  bodies  to  move  nearly  in  circles  and  others  to 
wander  toward  the  limits  of  the  solar  attraction,  and 
which  made  all  the  heavenly  bodies  to  rotate  and  re- 
volve in  the  same  direction,  must  have  had  their  origin 
in  the  primeval  state  of  things ;  but  as  it  pleases  the 
Supreme  Intelligence  to  employ  gravitation  alone  in  the 
maintenance  of  this  fair  system,  it  may  be  presumed  to 
have  presided  at  its  creation. 


SECTION  XXXVII. 

The  Fixed  Stars — Their  Numbers — Estimation  of  their  Distances  and 
Magnitudes  from  their  Light— Stars  that  have  vanished— New  Stars—- 
Double Stars— Binary  and  Multiple  Systems— Their  Orbits  and  Periods 
— Orbitual  and  Parallactic  Motions — Colors — Proper  Motions — General 
Motions  of  all  the  Stars — Clusters — Nebulae — Their  Number  and  Forms 
— Double  and  Stellar  Nebulae — Nebulous  Stars — Planetary  Nebulae — 
Constitution  of  the  Nebula?,  and  Forces  which  maintain  them— Distribu- 
tion— Meteorites — Shooting  Stars. 

GREAT  as  the  number  of  comets  appears  to  be,  it  is 
absolutely  nothing  when  compared  with  the  multitude  of 
the  fixed  stars.  About  2000  only  are  visible  to  the 
naked  eye  ;  but  when  we  view  the  heavens  with  a 
telescope,  their  number  seems  to  be  limited  only  by  the 
imperfection  of  the  instrument.  In  one  hour  Sir  Wil- 
liam Herschel  estimated  that  50,000  stars  passed  through 
the  field  of  his  telescope,  in  a  zone  of  the  heavens  2°  in 
breadth.  This,  however,  was  stated  as  an  instance  of 
extraordinary  crowding ;  but,  on  an  average,  the  whole 
expanse  of  the  heavens  must  exhibit  about  a  hundred 
millions  of  fixed  stars  within  the  reach  of  telescopic 
vision. 

The  stars  are  classed  according  to  their  apparent 
brightness,  and  the  places  of  the  most  remarkable  of 
those  visible  to  the  naked  eye  are  ascertained  with 
great  precision,  and  formed  into  a  catalogue,  not  only 
for  the  determination  of  geographical  positions  by  their 
occultations,  but  to  serve  as  points  of  reference  for 
marking  the  places  of  comets  and  other  celestial  phe- 
HH 


362  DISTANCE  OF  THE  STARS.        SECT.  XXXVII. 

nomena.  The  whole  number  of  stars  registered  amounts 
to  about  150,000  or  200,000.  The  distance  of  the  fixed 
stars  is  too  great  to  admit  of  their  exhibiting  a  sensible 
disc  ;  but  in  all  probability  they  are  spherical,  and  must 
certainly  be  so  if  gravitation  pervades  all  space,  which  it 
may  be  presumed  to  do,  since  Sir  John  Herschel  has 
shown  that  it  extends  to  the  binary  systems  of  stars. 
With  a  fine  telescope  the  stars  appear  like  a  point  of 
light ;  their  occultations  by  the  moon  are  therefore 
instantaneous.  Their  twinkling  arises  from  sudden 
changes  in  the  refractive  powers  of  the  air,  which  would 
not  be  sensible  if  they  had  discs  like  the  planets.  Thus 
we  can  learn  nothing  of  the  relative  distances  of  the 
stars  from  us,  and  from  one  another,  by  their  apparent 
diameters.  The  annual  parallax  of  all  but  a  very  few 
being  insensible,  shows  we  must  be  more  than  two 
hundred  millions  of  millions  of  miles  at  least  from  them. 
Many  of  them,  however,  must  be  vastly  more  remote ; 
for  of  two  stars  that  appear  close  together,  one  may  be 
far  beyond  the  other  in  the  depth  of  space.  The  light 
of  Sirius,  according  to  the  observations  of  Sir  John 
Herschel,  is  324  times  greater  than  that  of  a  star  of  the 
sixth  magnitude  ;  if  we  suppose  the  two  to  be  really  of 
the  same  size,  their  distances  from  us  must  be  in  the 
ratio  of  57-3  to  1,  because  light  diminishes  as  the  square 
of  the  distance  of  the  luminous  body  increases. 

Nothing  is  known  of  the  absolute  magnitude  of  the 
fixed  stars,  but  the  quantity  of  light  emitted  by  many 
of  them  shows  that  they  must  be  much  larger  than  the 
sun.  Dr.  Wollaston  determined  the  approximate  ratio* 
which  the  light  of  a  wax  candle  bears  to  that  of  the  sun, 
moon,  and  stars,  by  comparing  their  respective  images 
reflected  from  small  glass  globes  filled  with  mercury, 
whence  a  comparison  was  established  between  the 
quantities  of  light  emitted  by  the  celestial  bodies  them- 
selves. By  this  method  he  found  that  the  light  of  the 
sun  is  about  twenty  millions  of  millions  of  times  greater 
than  that  of  Sirius,  the  brightest  and  one  of  the  nearest 
of  the  fixed  stars.  Since  the  parallax  of  Sirius  is  about 
half  a  second,  its  distance  from  the  earth  must  be  592,200 
tim  es  the  distance  of  the  sun  from  the  earth ;  and 
therefore  Sirius,  placed  where  the  sun  is,  would  appear 


Sxcr.  XXXVII.     DISAPPEARANCE  OP  STARS  363 

to  us  to  be  3-7  times  as  large  as  the  sun,  and  would  give 
13-8  times  more  light.  Many  of  the  fixed  stars  must  be 
infinitely  larger  than  Sirius. 

Many  stars  have  vanished  from  the  heavens;  the 
star  42  Virginfs  seems  to  be  of  this  number,  having  been 
missed  by  Sir  John  Herschel  on  the  9th  of  May,  1828, 
and  not  again  found,  though  he  frequently  had  occasion 
to  observe  that  part  of  the  heavens.  Sometimes  stars 
have  all  at  once  appeared,  shone  with  a  bright  light, 
and  vanished.  Several  instances  of  these  temporary 
stars  are  on  record  ;  a  remarkable  instance  occurred  in 
the  year  125,  which  is  said  to  have  induced  Hipparchus 
to  form  the  first  catalogue  of  stars.  Another  star  ap- 
peared suddenly  near  a  Aquilae  in  the  year  389,  which 
vanished,  after  remaining  for  three  weeks  as  bright  as 
Venus.  On  the  10th  of  October,  1604,  a  brilliant  star 
burst  forth  in  the  constellation  of  Serpentarius,  which 
continued  visible  for  a  year;  and  a  more  recent  case 
occurred  in  the  year  1670,  when  a  new  star  was  discov- 
ered in  the  head  of  the  Swan,  which,  after  becoming 
invisible,  reappeared,  and  having  undergone  many  varia- 
tions in  light,  vanished  after  two  years,  and  has  never 
since  been  seen.  In  1572  a  star  was  discovered  in  Cas- 
siopeia, which  rapidly  increased  in  brightness  till  it  even 
surpassed  that  of  Jupiter  ;  it  then  gradually  diminished 
in  splendor,  and  having  exhibited  all  the  variety  of  tints 
that  indicate  the  changes  of  combustion,  vanished  sixteen 
months  after  its  discovery,  without  altering  its  position. 
It  is  impossible  to  imagine  anything  more  tremendous 
than  a  conflagration  that  could  be  visible  at  such  a  dis- 
tance. It  is  however  suspected  that  this  star  may  be 
periodical,  and  identical  with  the  stars  which  appeared 
in  the  years  945  and  1264.  There  are  probably  many 
stars  which  alternately  vanish  and  reappear  among  the 
innumerable  multitudes  that  spangle  the  heavens ;  the 
periods  of  several  have  already  been  pretty  well  ascer- 
tained. Of  these  the  most  remarkable  is  the  star  Omi- 
cron,  in  the  constellation  Cetus.  It  appears  about  twelve 
times  in  eleven  years,  and  is  of  variable  brightness,  some- 
times appearing  like  a  star  of  the  second  magnitude  ; 
but  it  does  not  always  attain  the  same  lustre,  nor  does 
it  increase  or  diminish  by  the  same  degrees.  Accord- 


364  VARIABLE  STARS.  SECT.  XXXVII. 

ing  to  Hevelius,  it  did  not  appear  at  all  for  four  years. 
y  Hydrae  also  vanishes  and  reappears  every  494  days : 
and  a  very  singular  instance  of  periodicity  is  given  by 
Sir  John  Herschel,  in  the  star  Algol  or  /3  Persei,  which 
is  described  as  retaining  the  size  of  a  star  of  the  second 
magnitude  for  two  days  and  fourteen  hours ;  it  then 
suddenly  begins  to  diminish  in  splendor,  and  in  about 
three  hours  and  a  half  is  reduced  to  the  size  of  a  star 
of  the  fourth  magnitude ;  it  then  begins  again  to  increase, 
and  in  three  hours  and  a  half  more  regains  its  usual 
brightness,  going  through  all  these  vicissitudes  in  two 
days,  twenty  hours,  and  forty-eight  minutes,  a  Cassi- 
opeia? is  also  periodical,  accomplishing  its  changes  in  225 
days  :  the  period  of  the  star  34  Cygni  is  18  years  ;  and 
Sir  John  Herschel  has  discovered  very  singular  varia- 
tions in  the  star  y  of  the  constellation  Argo.  It  is  sur- 
rounded by  a  wonderful  nebula,  and  from  a  star  of  little 
more  than  the  second  magnitude  it  suddenly  increased 
between  the  years  1837  and  1838  to  be  a  first-rate  star 
of  the  first  magnitude.  At  the  latter  period  it  was  equal 
to  Arcturus,  and  its  brilliancy  was  then  so  great  as  to 
obliterate  some  of  the  details  of  the  surrounding  nebula. 
Afterward  it  decreased  to  the  first  magnitude,  and  then 
began  to  increase  again.  Sir  John  has  also  discovered 
that  a  Orionis  may  now  be  classed  among  the  variable 
and  periodic  stars,  a  circumstance  the  more  remarkable, 
as  it  is  one  of  the  conspicuous  stars  of  our  hemisphere, 
and  yet  its  changes  had  never  been  remarked.  The 
inferences  Sir  John  draws  from  the  phenomena  of  vari- 
able stars  are  too  interesting  not  to  be  given  in  his  own 
words.  "  A  periodic  change  existing  to  so  great  an  ex- 
tent in  so  large  and  brilliant  a  star  as  a  Orionis,  cannot 
fail  to  awaken  attention  to  the  subject,  and  to  revive  the 
consideration  of  those  speculations  respecting  the  possi- 
bility of  a  change  in  the  lustre  of  our  sun  itself  which 
were  put  forth  by  my  father.  If  there  really  be  a  com- 
munity of  nature  between  the  sun  and  fixed  stars,  every 
proof  that  we  obtain  of  the  extensive  prevalence  of  such 
periodical  changes  in  those  remote  bodies  adds  to  the 
probability  of  finding  something  of  the  kind  nearer  home. 
If  our  sun  were  ever  intrinsically  much  brighter  than  at 
present,  the  mean  temperature  of  the  surface  of  our 


.  XXXViL  DOUBLE  STABS.  365 

globe  would  of  course  be  proportionally  greater.  I  speak 
now  not  of  periodical  but  secular  changes.  But  the  ar- 
gument is  complicated  with  the  consideration  of  the 
possibly  imperfect  transparency  of  the  celestial  spaces, 
and  with  the  cause  of  that  imperfect  transparency  which 
may  be  due  to  material  non-luminous  particles  diffused 
irregularly  in  patches  analogous  to  nebulae,  but  of  greater 
extent — to  cosmical  clouds  in  short — of  whose  existence 
we  have,  I  think,  some  indication  in  the  singular  and 
apparently  capricious  phenomena  of  temporary  stars, 
and  perhaps  in  the  recent  extraordinary  sudden  increase 
and  hardly  less  sudden  diminution  of  rj  Argus."  Mr. 
Goodricke  has  conjectured  that  the  periodical  changes 
in  the  stars  may  be  occasioned  by  the  revolution  of  some 
opaque  body  coming  between  us  and  the  star,  and  ob- 
structing part  of  its  light.  Sir  John  Herschel  is  struck 
with  the  high  degree  of  activity  evinced  by  these  changes 
in  regions  where,  "  but  for  such  evidences,  we  might 
conclude  all  to  be  lifeless."  He  observes  that  our  own 
sun  requires  nine  times  the  period  of  Algol  to  perform 
a  revolution  on  its  own  axis ;  while  on  the  other  hand, 
the  periodic  time  of  an  opaque  revolving  body  sufficiently 
large  to  produce  a  similar  temporary  obscuration  of  the 
sun,  seen  from  a  fixed  star,  would  be  less  than  fourteen 
hours. 

Many  thousands  of  stars  that  seem  to  be  only  brilliant 
points,  when  carefully  examined  are  found  to  be  in 
reality  systems  of  two  or  more  suns,  sometimes  revolving 
about  a  common  center.  These  binary  and  multiple 
stars  are  extremely  remote,  requiring  the  most  power- 
ful telescopes  to  show  them  separately.  The  first  cat- 
alogue of  double  stars,  in  which  their  places  and  relative 
positions  are  determined,  was  accomplished  by  the  tal- 
ents and  industry  of  Sir  William  Herschel,  to  whom 
Astronomy  is  indebted  for  so  many  brilliant  discoveries, 
and  with  whom  the  idea  of  their  combination  in  binary 
and  multiple  systems  originated  —  an  idea  completely 
established  by  his  own  observations,  and  recently  con- 
firmed by  those  of  his  son  and  other  astronomers.  The 
motions  of  revolution  of  many  of  these  stars  round  a 
common  center  have  been  ascertained,  and  their  periods 
determined  with  considerable  accuracy.  Some  have, 


366  BINARY  SYSTEMS.  SECT.  XXXVII. 

since  their  first  discovery,  already  accomplished  nearly 
a  whole  revolution ;  and  one,  rj  Coronae,  is  actually  con- 
siderably advanced  in  its  second  period.  These  inte- 
resting systems  thus  present  a  species  of  sidereal  chro- 
nometer, by  which  the  chronology  of  the  heavens  will 
be  marked  out  to  future  ages  by  epochs  of  their  own, 
liable  to  no  fluctuations  from  such  planetary  disturbances 
as  take  place  in  our  system. 

In  observing  the  relative  position  of  the  stars  of  a  bi- 
nary system,  the  distance  between  them,  and  also  the 
angle  of  position,  that  is,  the  angle  which  the  meridian 
or  a  parallel  to  the  equator  makes  with  the  line  joining 
the  two  stars,  are  measured.  The  different  values  of 
the  angle  of  position  show  whether  the  revolving  star 
moves  from  east  to  west,  or  the  contrary  ;  whether  the 
motion  be  uniform  or  variable,  and  at  what  points  it  is 
greatest  or  least.  The  measures  of  the  distances  show 
whether  the  two  stars  approach  or  recede  from  one 
another.  From  these  the  form  and  nature  of  the  orbit 
are  determined.  Were  observations  perfectly  accurate, 
four  values  of  the  angle  of  position  and  of  the  corre- 
sponding distances  at  given  epochs  would  be  sufficient 
to  assign  the  form  and  position  of  the  curve  described 
by  the  revolving  star:  this,  however,  scarcely  ever 
happens.  The  accuracy  of  each  result  depends  upon 
taking  the  mean  of  a  great  number  of  the  best  observa- 
tions, and  eliminating  error  by  mutual  comparison.  The 
distances  between  the  stars  are  so  minute  that  they  can- 
not be  measured  with  the  same  accuracy  as  the  angles 
of  position  ;  therefore,  to  determine  the  orbit  of  a  star 
independently  of  the  distance,  it  is  necessary  to  assume 
as  the  most  probable  hypothesis,  that  the  stars  are  sub- 
ject to  the  law  of  gravitation,  and  consequently  that  one 
of  the  two  stars  revolves  in  an  ellipse  about  the  other, 
supposed  to  be  at  rest,  though  not  necessarily  in  the  fo- 
cus. A  curve  is  thus  constructed  graphically  by  means 
of  the  angles  of  position  and  the  corresponding  times  of 
observation.  The  angular  velocities  of  the  «tars  are 
obtained  by  drawing  tangents  to  this  curve  at  stated  in- 
tervals, whence  the  apparent  distances,  or  radii  vectores, 
of  the  revolving  star  become  known  for  each  angle  of 
position ;  because,  by  the  laws  of  elliptical  motion,  they 


S*cr.  XXXVH.  BINARY  SYSTEMS.  367 

are  equal  to  the  square  roots  of  the  apparent  angular 
velocities.  Now  that  the  angles  of  position  estimated 
from  a  given  line,  and  the  corresponding  distances  of  the 
two  stars,  are  known,  another  curve  may  be  drawn, 
which  will  represent  on  paper  the  actual  orbit  of  the 
star  projected  on  the  visible  surface  of  the  heavens ;  so 
that  the  elliptical  elements  of  the  true  orbit  and  its  posi- 
tion in  space  may  be  determined  by  a  combined  system 
of  measurements  and  computation.  But  as  this  orbit 
has  been  obtained  on  the  hypothesis  that  gravitation 
prevails  in  these  distant  regions,  which  could  not  be 
known  d  priori,  it  must  be  compared  with  as  many 
observations  as  can  be  obtained,  to  ascertain  how  far  the 
computed  ellipse  agrees  with  the  curve  actually  described 
by  the  star. 

By  this  process  Sir  John  Herschel  has  discovered 
that  several  of  these  systems  of  stars  are  subject  to  the 
same  laws  of  motion  with  our  system  of  planets  :  he  has 
determined  the  elements  of  their  elliptical  orbits,  and 
computed  the  periods  of  their  revolution.  One  of  the 
stars  of  y  Virginis  revolves  about  the  other  hi  629  years  ; 
the  periodic  time  of  a  Corona?  is  287  years ;  that  of 
Castor  is  253  years;  that  of  t  Bootes  is  1600 ;  that  of 
70  Ophiuchi  is  ascertained  by  Professor  Encke  to  be  80 
years ;  Professor  Bessel  has  ascertained  the  period  of 
61  Cygni  to  be  540  years  ;  and  M.  Savary,  who  has  the 
merit  of  having  first  determined  the  elliptical  elements 
of  the  orbit  of  a  binary  star  from  observation,  has  shown 
that  the  revolution  of  f  Ursae  is  completed  in  58  years. 
y  Virginis  consists  of  two  stars  of  nearly  the  same  mag- 
nitude. They  were  so  far  apart  in  the  beginning  and 
middle  of  the  last  century,  that  they  were  mentioned  by 
Bradley  and  marked  in  Mayer's  catalogue  as  two  distinct 
stars.  Now,  they  are  so  near  to  one  another,  that  even 
with  good  telescopes  they  look  like  a  single  star  some- 
what elongated.  A  series  of  observations,  since  the 
beginning  of  the  present  century,  has  enabled  Sir  John 
Herschel  to  determine  the  form  and  position  of  the  el- 
liptical orbit  of  the  revolving  star  with  extraordinary 
truth.  According  to  his  computation,  it  must  have  ar- 
rived at  its  perihelion  on  the  18th  of  August  of  the  year 
3  834.  The  actual  proximity  of  the  two  stars  must  then 


368  ORBITS  OF  DOUBLE  STARS.      SECT.  XXXVII. 

have  been  extreme,  and  the  apparent  angular  velocity 
so  great  that  it  might  have  described  an  angle  of  68°  in 
a  single  year.  Observations  made  at  the  Cape  of  Good 
Hope,  by  Sir  John  Herschel,  as  well  as  those  of  Captain 
Smyth,  R.  N.,  at  home,  correspond  in  proving  an  aug- 
mentation of  velocity  as  the  star  was  approaching  its 
shortest  distance  from  its  primary.  By  the  laws  of  el- 
liptical motion,  the  angular  velocity  of  the  revolving  star 
must  now  gradually  diminish,  till  it  comes  to  its  aphelion 
some  314  years  hence.  The  satellite  star  of  a  Coronae 
attained  its  perihelion  in  1835,  and  that  of  Castor  will  do 
the  same  some  time  in  1855. 

It  sometimes  happens  that  the  edge  of  the  orbit  of«  a 
revolving  star  is  presented  to  the  earth,  as  in  TT  Serpen- 
tarii.  Then  the  star  seems  to  move  in  a  straight  line, 
and  to  oscillate  on  each  side  of  its  primary.  Five  ob- 
servations are  requisite  in  this  case  for  the  determina- 
tion of  its  orbit,  provided  they  be  accurate.  At  the  time 
Sir  William  Herschel  observed  the  system  in  question, 
the  two  stars  were  distinctly  separate  :  at  present,  one 
is  so  completely  projected  on  the  other,  that  M.  Struve, 
with  his  great  telescope,  cannot  perceive  the  smallest 
separation.  On  the  contrary,  the  two  stars  of  C  Orionis, 
which  appeared  to  be  one  in  the  time  of  Sir  William 
Herschel,  are  now  separated.  Were  this  lib  ration  owing 
to  parallax,  it  would  be  annual,  from  the  revolution  of  the 
earth  ;  but  as  years  elapse  before  it  amounts  to  a  sensi- 
ble quantity,  it  can  only  arise  from  a  real  orbitual  motion 
seen  obliquely.  Among  the  triple  stars,  two  of  the  stars  of 
£  Cancri  revolve  about  the  third.  There  are  also  quadru- 
ple stars,  and  there  are  even  assemblages  of  five  and  six 
stars,  as  6  and  or  of  Orion.  It  is  remarked  that,  in  gen- 
eral, the  ellipses  in  which  the  revolving  stars  of  binary 
systems  move,  are  much  more  elongated  than  the  orbits 
of  the  planets.  Sir  John  Herschel,  Sir  James  South, 
and  Professor  Struve  of  Dorpat,  have  increased  Sir 
William  Herschel's  original  catalogue  of  double  stars  to 
more  than  6000,  of  which  thirty  or  forty  are  known  to 
form  revolving  or  binary  systems  :  and  Mr.  Dunlop  has 
formed  a  catalogue  of  253  double  stars  in  the  southern 
hemisphere.  To  this  Sir  John  Herschel  has  added 
many ;  but  he  has  found  that  the  southern  hemisphere 


Stcr.  XXXVII.  PROPER  MOTIONS  OF  THE  STARS.  369 

is  poorer  than  the  northern  in  close  double  stars  above 
the  tenth  magnitude.  He  observes,  that  if  Mr.  Dunlop's 
measures  can  be  depended  upon,  6  Eridani  is  perhaps 
the  most  remarkable  of  all  the  binary  systems  in  the 
heavens.  The  revolution  of  the  satellite  star  being  at 
the  rate  of  10°-67  per  annum,  it  consequently  must 
accomplish  a  revolution  in  a  little  more  than  thirty  years. 
The  motion  of  Mercury  is  more  rapid  than  that  of  any- 
other  planet,  being  at  the  rate  of  107,000  miles  an  hour ; 
the  perihelion  velocity  of  the  comet  of  1680  was  no  less 
than  880,000  miles  an  hour ;  but  if  the  two  stars  of  6 
Eridani  or  £  Ursae  be  as  remote  from  one  another  as  the 
nearest  fixed  star  is  from  the  sun,  the  velocity  of  the 
revolving  stars  must  exceed  the  powers  of  imagination. 
The  discovery  of  the  elliptical  motion  of  the  double  stars 
excites  the  highest  interest,  since  it  shows  that  gravita- 
tion is  not  peculiar  to  our  system  of  planets,  but  that 
systems  of  suns  in  the  far  distant  regions  of  the  uni- 
verse are  also  obedient  to  its  laws. 

Besides  revolutions  about  one  another,  some  of  the 
binary  systems  are  carried  forward  in  space  by  a  motion 
common  to  both  stars,  toward  some  unknown  point  in 
the  firmament.  The  two  stars  of  61  Cygni,  which  are 
nearly  equal,  and  have  remained  at  the  distance  of  about 
15"  from  each  other  for  fifty  years,  have  changed  their 
place  in  the  heavens  during  that  period,  by  4'  23",  with 
a  motion  which  for  ages  must  appear  rectilinear :  be- 
cause, even  if  the  path  be  curved,  so  small  a  portion  of 
it  must  appear  a  straight  line  to  us.  The  single  stars 
also  have  proper  motions,  yet  so  minute  that  the  trans- 
lation of  p  Cassiopeiae,  of  3"'74  annually,  is  the  greatest 
yet  observed :  but  the  enormous  distances  of  the  stars 
make  motions  appear  small  to  us  which  are  in  reality 
very  great.  Sir  William  Herschel  conceived  that, 
among  many  irregularities,  the  motions  of  the  stars  have 
a  general  tendency  toward  a  point  diametrically  oppo- 
site to  that  occupied  by  the  star  £  Herculis,  which  he 
attributed  to  a  motion  of  the  solar  system  in  the  contrary 
direction.  Should  this  really  be  the  case,  the  stars, 
from  the  effects  of  perspective  alone,  would  seem  to 
diverge  in  the  direction  to  which  we  are  tending,  and 
would  apparently  converge  in  the  space  we  leave,  and 
24 


370  PROPER  MOTIONS  OF  THE  STARS.    SECT.  XXXVII. 

there  would  be  a  regularity  in  these  apparent  motions 
which  would  in  time  be  detected ;  but  if  the  solar  sys- 
tem and  the  whole  of  the  stars  visible  to  us  be  carried 
forward  in  space  by  a  motion  common  to  all,  like  ships 
drifting  in  a  current,  it  would  be  impossible  for  us, 
moving  with  the  rest,  to  ascertain  its  direction.  There 
can  be  no  doubt  of  the  progressive  motion  of  the  sun  and 
stars,  but  sidereal  astronomy  is  not  far  enough  advanced 
to  determine  what  relations  these  bear  to  one  another ; 
it  will  however  be  known  in  the  course  of  time  from  the 
orbits  of  the  revolving  stars  of  the  binaiy  systems.  For 
if  the  solar  system  be  in  motion,  some  of  the  stellar 
orbits  which,  by  the  effects  of  perspective,  appear  to  us 
to  be  straight  lines,  will,  after  a  time,  open  and  become 
elliptical  by  our  change  of  place  ;  while  others  which 
now  appear  to  be  open  will  close,  or  open  wider ;  stars 
also  which  now  occultate,  or  hide  one  another  in  certain 
points  of  their  orbits,  will,  in  time,  cease  to  do  so.  The 
directions  and  magnitude  of  these  changes  will  no  doubt 
show  the  motion  of  our  system,  to  what  point  it  is  tend- 
ing, and  the  velocity  with  which  it  moves. 

Among  the  multitudes  of  small  stars,  whether  double 
or  insulated,  a  few  are  found  near  enough  to  exhibit 
distinct  parallactic  motions,  arising  from  the  revolution 
of  the  earth  in  its  orbit.  Of  two  stars  apparently  in 
close  approximation,  one  may  be  far  behind  the  other  in 
space.  These  may  seem  near  to  one  another  when 
viewed  from  the  earth  in  one  part  of  its  orbit,  but  may 
separate  widely  when  seen  from  the  earth  in  another 
position,  just  as  two  terrestrial  objects  appear  to  be  one 
when  viewed  in  the  same  straight  line,  but  separate  as 
the  observer  changes  his  position.  In  this  case  the  stars 
would  not  have  real,  but  only  apparent  motion.  One  of 
them  would  seem  to  oscillate  annually  to  and  fro  in  a 
straight  line  on  each  side  of  the  other — a  motion  which 
could  not  be  mistaken  for  that  of  a  binary  system, 
where  one  star  describes  an  ellipse  about  the  other,  or, 
if  the  edge  of  the  orbit  be  turned  toward  the  earth, 
where  the  oscillations  require  years  for  their  accom- 
plishment. 

This  method  of  finding  the  distances  of  the  fixed  stars 
was  proposed  by  Galileo,  and  attempted  by  Dr.  Long 


SKCT.  XXXVII.   DISTANCE  OF  BINARY  SYSTEMS.  371 

without  success.  Sir  William  Herschel  afterward  ap- 
plied it  to  some  of  the  binary  groups ;  and  though  he 
did  not  find  the  thing  he  sought  for,  it  led  to  the  dis- 
covery of  the  orbitual  motions  of  the  double  stars. 

Though  the  absolute  distance  of  most  of  the  stars  is 
still  a  desideratum,  a  limit  has  been  found  under  which, 
probably,  none  of  them  come.  It  was  natural  to  sup- 
pose that  in  general  the  large  stars  are  nearer  to  the 
earth  than  the  small  ones ;  but  there  is  now  reason  to 
believe  that  some  stars,  though  by  no  means  brilliant, 
are  nearer  to  us  than  others  which  shine  with  greater 
splendor.  This  is  inferred  from  the  comparative  ve- 
locity of  their  motions.  All  the  stars  have  a  general 
motion  of  translation,  which  tends  ultimately  to  mix  the 
stars  of  the  different  constellations,  but  none  that  we 
know  of  moves  so  rapidly  as  61  Cygni;  and  on  that 
account  it  is  reckoned  to  be  nearer  to  us  than  any 
other,  for  an  object  seems  to  move  more  quickly  the 
nearer  we  are  to  it.  This  circumstance  induced  MM. 
Arago  and  Mathieu  to  endeavor  to  determine  its  an- 
nual parallax,  that  is,  to  ascertain  what  magnitude  the  di- 
ameter of  the  earth's  orbit  would  have  as  seen  from  the 
star,  and  from  that  to  compute  its  distance  from  the 
earth  (N.  223).  This  has  been  accomplished  with  more 
accuracy  by  M.  Bessel,  who  has  found  by  observation, 
that  the  diameter  of  the  earth's  orbit  of  190  millions  of 
miles  would  be  seen  from  the  star  under  an  angle  of 
only  one-third  of  a  second,  whence  61  Cygni  must  be 
592,200  times  farther  from  the  earth  than  the  sun  is, 
— a  distance  which  light,  flying  at  the  rate  of  190,000 
miles  in  a  second,  would  not  pass  over  in  less  than 
nine  years  and  three  months. 

The  apparent  motion  of  five  seconds  annually  which 
this  star  has,  seems  to  us  to  be  extremely  small,  but  at  that 
distance  an  angle  of  one  second  corresponds  to  twenty- 
four  millions  of  millions  of  miles  ;  consequently  the  an- 
nual motion  of  61  Cygni  is  one  hundred  and  twenty 
millions  of  millions  of  miles,  and  yet,  as  M.  Arago  ob- 
serves, we  call  it  a  fixed  star  ! 

From  the  observations  of  Professor  Henderson  it  ap- 
pears that  Sirius,  the  brightest  star  in  the  heavens,  has 
a  parallax  of  less  than  the  third  of  a  second ;  conse- 


372  DISTANCE  OF  BINARY  SYSTEMS.  SECT.  XXXVIL 

quently  it  is  at  a  greater  distance  than  61  Cygni :  that 
of  a  Centauri  amounts  to  a  second  of  space,  so  that  it  is 
nearer  the  earth  than  any  star  that  is  known :  whereas 
Mr.  Airy  has  found  that  the  parallax  of  a  Lyra?  is  al- 
together inappreciable  ;  and  as  this  is  generally  the  case 
with  the  fixed  stars,  we  may  conclude  that  their  dis- 
tances are  beyond  the  hope  of  mensuration. 

All  the  ordinary  methods  fail  when  the  distances  are 
so  enormous.  An  angle  even  of  two  or  three  seconds, 
viewed  in  the  focus  of  our  largest  telescopes,  does  not 
equal  the  thickness  of  a  spider's  thread,  which  makes  it 
impossible  to  measure  such  minute  quantities  with  any 
degree  of  accuracy.  In  some  cases,  however,  the  bi- 
nary systems  of  stars  furnish  a  method  of  estimating  an 
angle  of  even  the  tenth  of  a  second,  which  is  thirty 
times  more  accurate  than  by  any  other  means.  From 
them  the  actual  distances  of  some  of  the  more  remote 
stars  will  ultimately  be  known. 

Suppose  that  one  star  revolves  about  another  in  an 
orbit  which  is  so  obliquely  seen  from  the  earth  as  to 
look  like  an  ellipse  in  a  horizontal  position,  then  it  is 
clear  that  one  half  of  the  orbit  will  be  nearer  to  us  than 
the  other  half.  Now,  in  consequence  of  the  time  which 
light  takes  to  travel,  we  always  see  the  satellite  star  in 
a  place  which  it  has  already  left.  Hence  when  that 
star  sets  out  from  the  point  of  its  orbit  which  is  nearest 
to  us,  its  light  will  take  more  and  more  time  to  come  to 
us  in  proportion  as  the  star  moves  round  to  the  most 
distant  point  in  its  orbit.  On  that  account  the  star  will 
appear  to  us  to  take  more  time  in  moving  through  that 
half  of  its  orbit  than  it  really  does.  Exactly  the  con- 
trary takes  place  in  the  other  half:  for  the  light  will 
take  less  and  less  time  to  arrive  at  the  earth  in  propor- 
tion as  the  star  approaches  nearer  to  us,  and  therefore 
it  will  seem  to  move  through  this  half  of  its  orbit  in  less 
time  than  it  really  does.  This  circumstance  furnishes 
the  means  of  finding  the  absolute  breadth  of  the  orbit  in 
miles,  and  from  that  the  true  distance  of  the  star  from 
the  earth.  For,  since  the  greatest  and  least  distances 
of  the  satellite  star  from  the  earth  differ  by  the  breadth 
of  its  orbit,  the  time  which  the  star  takes  to  move  from 
the  nearest  to  the  remotest  point  of  its  orbit  is  greater  than 


SKCT.  XXXVII.  DISTANCE  OF  BINARY  SYSTEMS.  373 

it  ought  to  be,  by  the  whole  time  its  light  takes  to  cross 
the  orbit,  and  the  period  of  moving  through  the  other 
half  is  exactly  as  much  less.  Hence  the  difference  be- 
tween the  observed  times  of  these  two  semi-revolutions 
of  the  star  is  equal  lo  twice  the  time  thai  its  light  em- 
ploys to  cross  its  orbit;  and  as  we  know  the  velocity  of 
light,  the  diameter  of  the  orbit  may  be  found  in  miles, 
and  from  that  its  whole  dimensions.  For  the  position  of 
the  orbit  with  regard  to  us  is  known  by  observation,  as 
well  as  the  place,  inclination,  and  apparent  magnitude 
of  its  major  axis,  or,  which  is  the  same  thing,  the  angle 
under  which  it  is  seen  from  the  earth.  Since,  then, 
three  things  are  known  in  this  great  triangle,  namely, 
the  base  or  major  axis  of  the  orbit  in  miles,  the  angle 
opposite  to  it  at  the  earth,  and  the  angle  it  makes  with 
the  visual  ray ;  the  distance  of  the  satellite  star  from  the 
earth  may  be  found  by  the  most  simple  of  calculations. 
The  merit  of  having  first  proposed  this  veiy  ingenious 
method  of  finding  the  distances  of  the  stars  is  due  to  M. 
Savary ;  but  unfortunately  it  is  not  of  general  application, 
as  it  depends  upon  the  position  of  the  orbit,  and  even 
then  a  long  time  must  elapse  before  observation  can  fur- 
nish data,  since  the  shortest  period  of  any  revolving  star 
that  we  know  of  is  thirty  years  :  still  the  distances  of  a 
vast  number  of  stars  may  be  ultimately  made  out  in  this 
way  ;  and  as  one  important  discovery  almost  always  leads 
to  another,  their  masses  may  thus  be  weighed  against 
that  of  the  earth  or  sun. 

The  only  data  employed  for  finding  the  mass  of  the 
earth,  as  compared  with  that  of  the  sun,  are  the  angular 
motion  of  our  globe  round  the  sun  in  a  second  of  time, 
and  the  distance  of  the  earth  from  the  sun  in  miles  (N. 
224).  Now  by  the  observations  of  the  binary  systems, 
we  know  the  angular  velocity  of  the  small  star  round 
the  great  one ;  and  when  we  know  the  distance  between 
the  two  stars  in  miles,  it  will  be  easy  to  compute  how 
many  miles  the  small  star  would  fall  through  by  the  at- 
traction of  the  great  one  in  a  second  of  time.  A  compar- 
ison of  this  space  with  the  space  which  the  earth  would 
descend  through  in  a  second  toward  the  sun,  will  give 
the  ratio  of  the  mass  of  the  great  star  to  that  of  the  sun 
or  earth. 

Ii 


374  COLORS  OF  THE  STARS.          SECT.  XXXVII. 

If  it  be  considered  that  all  the  double  stars  appear  sin- 
gle to  the  naked  eye,  and  with  ordinary  instruments, 
and  that  it  requires  the  highest  powers  of  the  very  best 
telescopes  to  separate  the  greater  number  of  them,  the 
extreme  beauty  of  the  ingenuity  and  refraction  necessary 
to  draw  such  profound  results  from  their  motions  may 
be  in  some  degree  appreciated. 

The  double  stars  are  of  various  hues,  but  they  most 
frequently  exhibit  the  contrasted  colors.  The  large  star 
is  generally  yellow,  orange,  or  red ;  and  the  small  star 
blue,  purple,  or  green.  Sometimes  a  white  star  is  com- 
bined with  a  blue  or  purple,  and  more  rarely  a  red  and 
white  are  united.  In  many  cases,  these  appearances 
are  due  to  the  influence  of  contrast  on  our  judgment  of 
colors.  For  example,  in  observing  a  double  star,  where 
the  large  one  is  a  full  ruby  red,  or  almost  blood  color, 
and  the  small  one  a  fine  green,  the  latter  loses  its  color 
when  the  former  is  hid  by  the  cross  wires  of  the  tele- 
scope. But  there  are  avast  number  of  instances  where 
the  colors  are  too  strongly  marked  to  be  merely  imagi- 
nary. Sir  John  Herschel  observes  in  one  of  his  papers 
in  the  Philosophical  Transactions,  as  a  very  remarkable 
fact,  that,  although  red  stars  are  common  enough,  no 
example  of  a  solitary  blue,  green,  or  purple  one  has  yet 
been  produced. 

The  stars  are  scattered  very  irregularly  over  the  fir- 
mament. In  some  places  they  are  crowded  together,  in 
others  thinly  dispersed.  A  few  groups  more  closely 
condensed  form  veiy  beautiful  objects  even  to  the  naked 
eye,  of  which  the  Pleiades  and  the  constellation  Coma 
Berenices  are  the  most  striking  examples ;  but  the 
greater  number  of  these  clusters  of  stars  appear  to  un- 
assisted vision  like  thin  white  clouds  or  vapor :  such 
is  the  milky  way,  which,  as  Sir  William  Herschel  has 
proved,  derives  its  brightness  from  the  diffused  light  of 
the  myriads  of  stars  that  form  it.  Most  of  these  stars 
appear  to  be  extremely  small,  on  account  of  their  enor- 
mous distances ;  and  they  are  so  numerous,  that,  ac- 
cording to  his  estimation,  no  fewer  than  50,000  passed 
through  the  field  of  his  telescope  in  the  course  of  one 
hour  in  a  zone  2°  broad.  This  singular  portion  of  the 
heavens,  constituting  part  of  our  firmament,  consists  of 


Sscr.  XXXVII.  CLUSTERS  OF  STARS.  375 

an  extensive  mass  of  stars,  whose  thickness  is  small  com- 
pared with  its  length  and  breadth ;  the  earth  is  placed 
near  the  point  where  it  diverges  into  two  branches,  and 
it  appears  to  be  much  more  splendid  in  the  Southern 
hemisphere  than  in  the  Northern.  Sir  John  Herschel 
says,  "  The  general  aspect  of  the  Southern  circumpolar 
regions  (including  in  that  expression  60°  or  70°  of  South 
polar  distance)  is  in  a  high  degree  rich  and  magnificent, 
owing  to  the  superior  brilliancy  and  large  development 
of  the  milky  way,  which,  from  the  constellation  of  Orion 
to  that  of  Antinous,  is  a  blaze  of  light,  strangely  in- 
terrupted, however,  with  vacant  and  entirely  starless 
patches,  especially  in  Scorpio,  near  Alpha  Centauri  and 
the  Cross,  while  to  the  north  it  fades  away  pale  and 
dim,  and  is  in  comparison  hardly  traceable.  I  think  it  is 
impossible  to  view  this  splendid  zone,  with  the  astonish- 
ingly rich  and  evenly  distributed  fringe  of  stars  of  the 
3rd  and  4th  magnitude,  which  forms  a  broad  skirt  to  its 
southern  border  like  a  vast  curtain,  without  an  impres- 
sion amounting  almost  to  conviction,  that  the  milky  way 
is  not  a  mere  stratum,  but  annular,  or  at  least  that  our 
system  is  placed  within  one  of  the  poorer  or  almost 
vacant  parts  of  its  general  mass,  and  that  eccentrically,  so 
as  to  be  much  nearer  to  the  region  about  the  Cross,  than 
to  that  diametrically  opposite  to  it."  The  cluster,  of 
which  our  sun  is  a  member,  and  which  includes  the 
milky  way,  and  all  the  stars  that  adorn  our  sky,  must  be 
of  enormous  extent,  since  the  sun  is  more  than  two  hun- 
dred thousand  times  farther  from  the  nearest  of  them 
than  he  is  from  the  earth ;  and  the  other  stars,  though 
apparently  so  close  together,  are  probably  separated  from 
one  another  by  distances  equally  great.  In  the  intervals 
between  the  stars  of  our  own  system  and  far  in  the  depths 
of  space,  many  clusters  of  stars  may  be  seen  like  white 
clouds  or  round  comets  without  tails,  either  by  unassisted 
vision  or  with  ordinary  telescopes  ;  but,  seen  with  pow- 
erful instruments,  Sir  John  Herschel  describes  them  as 
conveying  the  idea  of  a  globular  space  insulated  in  the 
heavens  and  filled  full  of  stars,  constituting  a  family  or 
society  apart  from  the  rest,  subject  only  to  its  own  in- 
ternal laws.  To  attempt  to  count  the  stars  in  one  of 
these  globular  clusters,  he  says,  would  be  a  vain  task, — 


376  NEBULAE.  SECT,  xxxvu. 

that  they  are  not  to  be  reckoned  by  hundreds : — on  a 
rough  computation,  it  appears  that  many  clusters  of  this 
description  must  contain  ten  or  twenty  thousand  stars 
compacted  and  wedged  together  in  a  round  space, 
whose  area  is  not  more  than  a  tentiypart  of  that  covered 
by  the  moon ;  so  that  its  center,  where  the  stars  are 
seen  projected  on  each  other,  is  one  blaze  of  light 
(N.  225).  If  each  of  these  stars  be  a  sun,  and  if  they 
be  separated  by  intervals  equal  to  that  which  separates 
our  sun  from  the  nearest  fixed  star,  the  distance  which 
renders  the  whole  cluster  barely  visible  to  the  naked  eye 
must  be  so  great,  that  the  existence  of  this  splendid  as- 
semblage can  only  be  known  to  us  by  light  which  must 
have  left  it  at  least  a  thousand  years  ago.  Occasionally 
clusters  are  so  irregular  and  so  undefined  in  their  outline 
as  merely  to  suggest  the  idea  of  a  richer  part  of  the 
heavens.  These  contain  fewer  stars  than  the  globular 
clusters,  and  sometimes  a  red  star  forms  a  conspicuous 
object  among  them.  Sir  William  Herschel  regarded 
them  as  the  rudiments  of  globular  clusters  in  a  less  ad- 
vanced state  of  condensation,  but  tending  to  that  form 
by  their  mutual  attraction. 

Multitudes  of  nebulous  spots  are  to  be  seen  on  the 
clear  vault  of  heaven,  which  have  every  appearance  of 
being  clusters  like  those  described,  but  are  too  distant  to 
be  resolved  into  stars  by  the  most  excellent  telescopes. 
Vast  numbers  also  appear  to  be  matter  in  the  highest 
possible  degree  of  rarefaction,  giving  no  indication  what- 
ever of  a  stellar  nature.  These  are  in  every  state  of 
condensation,  from  a  vague  film  hardly  to  be  discerned 
with  telescopes  of  the  highest  powers,  to  such  as  seem 
to  have  actually  arrived  at  a  solid  nucleus.  This  nebu- 
lous matter  exists  in  vast  abundance  in  space.  No 
fewer  than  2000  nebulae  and  clusters  of  stars  were  ob- 
served by  Sir  William  Herschel,  whose  places  have 
been  computed  from  his  observations,  reduced  to  a  com- 
mon epoch,  and  arranged  into  a  catalogue  in  order  of 
right  ascension  by  his  sister,  Miss  Caroline  Herschel,  a 
lady  eminent  for  astronomical  knowledge  and  discovery. 
Six  or  seven  hundred  nebulae  have  already  been  ascer- 
tained in  the  southern  hemisphere ;  of  these  the  Ma- 
gellanic  clouds  are  the  most  remarkable.  The  nature 


SKCT.  XXXVH.  NEBULA.  377 

and  use  of  this  nebulous  matter,  scattered  over  the 
heavens  in  such  a  variety  of  forms,  is  involved  in  the 
greatest  obscurity.  That  it  is  a  self-luminous,  phos- 
phorescent, material  substance,  in  a  highly  dilated  or 
gaseous  state,  but  gradually  subsiding  by  the  mutual 
gravitation,  of  its  particles  into  stars  and  sidereal  systems, 
is  the  hypothesis  most  generally  received.  And  indeed 
this  is  the  hypothesis  of  La  Place  with  regard  to  the 
origin  of  the  solar  system,  which  he  conceived  to  be 
formed  by  the  successive  condensations  of  a  nebula, 
whose  primeval  rotation  is  still  maintained  in  the  rota- 
tion and  revolution  of  the  sun  and  all  the  bodies  of  the 
solar  system  in  the  same  direction.  Even  at  this  day 
there  is  presumptive  evidence  in  the  structure  and  in- 
ternal heat  of  the  earth,  of  its  having  been  at  one  period 
in  a  gaseous  state  from  intensely  high  temperature. 
But  the  only  way  that  any  real  knowledge  on  this  mys- 
terious subject  can  be  obtained  is  by  the  determination 
of  the  form,  place,  and  present  state  of  each  individual 
nebula ;  and  a  comparison  of  these  with  future  observa- 
tions will  show  generations  to  come  the  changes  that 
may  now  be  going  on  in  these  supposed  rudiments  of 
future  systems.  With  this  view,  Sir  John  Herschel 
began  in  the  year  1825  the  arduous  and  pious  task  of 
revising  his  illustrious  father's  observations,  Avhich  he 
finished  a  short  time  before  he  sailed  for  the  Cape  of 
Good  Hope,  in  order  to  disclose  the  mysteries  of  the 
southern  hemisphere  ;  indeed,  our  firmament  seems  to 
be  exhausted  till  farther  improvements  in  the  telescope 
shall  enable  astronomers  to  penetrate  deeper  into  space. 
In  a  truly  splendid  paper  read  before  the  Royal  Society 
on  the  21st  of  November,  1833,  he  gives  the  places  of 
2500  nebulae  and  clusters  of  stars.  Of  these  500  are 
neWj — the  rest  he  mentions  with  peculiar  pleasure  as 
having  been  most  accurately  determined  by  his  father. 
This  work  is  the  more  extraordinary,  as  from  bad 
weather,  fogs,  twilight,  and  moonlight,  these  shadowy 
appearances  are  not  visible,  on  an  average,  in  England, 
above  thirty  nights  in  the  year. 

The  nebulae  have  great  variety  of  forms.     Vast  multi- 
tudes are  so  faint  as  to  be  with  difficulty  discerned  at  all 
till  they  have  been  for  some  time  in  the  field  of  the 
u2 


378  FORMS  OF  THE  NEBULAE.        SECT.  XXXVII. 

telescope,  or  are  just  about  to  quit  it.  Occasionally 
they  are  so  vague  that  the  eye  is  conscious  of  some- 
thing, without  being  able  to  define  what  it  is :  but  the 
unchangeableness  of  its  position  proves  that  it  is  a  real 
object.  Many  present  a  large  ill-defined  surface,  in 
which  it  is  difficult  to  say  where  the  center  of  the 
greatest  brightness  is.  Some  cling  to  stars  like  wisps  of 
cloud ;  others  exhibit  the  wonderful  appearance  of  an 
enormous  flat  ring  seen  very  obliquely,  with  a  lenticular 
vacancy  in  the  center  (N.  226).  A  very  remarkable  in- 
stance of  an  annular  nebula  is  to  be  seen  exactly  half- 
way between  /9  and  y  Lyrae.  It  is  elliptical  in  the  ratio 
of  4  to  5,  and  is  sharply  defined,  the  internal  opening  oc- 
cupying about  half  the  diameter.  This  opening  is  not 
entirely  dark,  but  filled  up  with  a  faint  hazy  light,  aptly 
compared  by  Sir  John  Herschel  to  fine  gauze  stretched 
over  a  hoop  (N.  227).  There  is  a  very  remarkable 
nebula  in  Orion,  in  which  there  is  some  reason  to  believe 
that  a  new  star  has  recently  appeared.  Two  nebulae 
are  described  as  most  amazing  objects  : — One  like  a 
dumb-bell  or  hour-glass  of  bright  matter,  surrounded  by 
a  thin  hazy  atmosphere,  so  as  to  give  the  whole  an  oval 
form,  or  the  appearance  of  an  oblate  spheroid.  This 
phenomenon  bears  no  resemblance  to  any  known  object 
(N.  228).  The  other  consists  of  a  bright  round  nucleus, 
surrounded  at  a  distance  by  a  nebulous  ring  split  through 
half  its  circumference,  and  having  the  split  portions  sep- 
arated at  an  angle  of  45°  each  to  the  plane  of  the  other. 
This  nebula  bears  a  strong  similitude  to  the  milky  way, 
and  suggested  to  Sir  John  Herschel  the  idea  of  a 
"  brother  system  bearing  a  real  physical  resemblance 
and  strong  analogy  of  structure  to  our  own"  (N.  229). 
It  appears  that  double  nebulae  are  not  unfrequent,  ex- 
hibiting all  the  varieties  of  distance,  position,  and  relative 
brightness  with  their  counterparts  the  double  stars.  The 
rarity  of  single  nebulae  as  large,  faint,  and  as  little  con- 
densed in  the  center  as  these,  makes  it  very  improbable 
that  two  such  bodies  should  be  accidentally  so  near  as 
to  touch,  and  often  in  part  to  overlap  each  other,  as  these 
do.  It  is  much  more  likely  that  they  constitute  systems  ; 
and  if  so,  it  will  form  an  interesting  subject  of  future  in- 
quiry to  discover  whether  they  possess  orbitual  motion. 


Sscr.  XXXVII.   STELLAR  AND  PLANETARY  NEBULAE.       379 

Stellar  nebulae  form  another  class.  These  have  a 
round  or  oval  shape,  increasing  in  density  toward  the 
center.  Sometimes  the  matter  is  so  rapidly  condensed 
as  to  give  the  whole  the  appearance  of  a  star  with  a  blur, 
or  like  a  candle  shining  through  horn.  In  some  in- 
stances the  central  matter  is  so  highly  and  suddenly 
condensed,  so  vivid  and  sharply  defined,  that  the  nebula 
might  be  taken  for  a  bright  star  surrounded  by  a  thin 
atmosphere.  Such  are  nebulous  stars.  The  zodiacal 
light,  or  lenticular-shaped  atmosphere  of  the  sun,  which 
may  be  seen  extending  beyond  the  orbits  of  Mercury 
and  Venus  soon  after  sunset  in  the  months  of  April  and 
May,  is  supposed  to  be  a  condensation  of  the  ethereal 
medium  by  his  attractive  force,  and  seems  to  place  our 
sun  among  the  class  of  stellar  nebulas.  The  stellar  neb- 
ulae and  nebulous  stars  assume  all  degrees  of  ellipticity. 
Not  unfrequently  they  are  long  and  narrow,  like  a 
spindle-shaped  ray,  with  a  bright  nucleus  in  the  center 
(N.  230).  The  last  class  mentioned  by  Sir  John  Her- 
schel  are  the  planetary  nebulae.  These  bodies  have 
exactly  the  appearance  of  planets,  with  sensibly  round 
or  oval  discs,  sometimes  sharply  terminated,  at  other 
times  hazy  and  ill-defined.  Their  surface,  which  is 
blue  or  bluish  white,  is  equable  or  slightly  mottled,  and 
their  light  occasionally  rivals  that  of  the  planets  in  vivid- 
ness. They  are  generally  attended  by  minute  stars, 
which  give  the  idea  of  accompanying  satellites.  These 
nebulae  are  of  enormous  dimensions.  One  of  them  near 
v  Aquarii  has  a  sensible  diameter  of  about  20",  and 
another  presents  a  diameter  of  12".  Sir  John  Her- 
schel  has  computed  that,  if  these  objects  be  as  far  from 
us  as  the  stars,  their  real  magnitude,  on  the  lowest  esti- 
mation, must  be  such  as  would  fill  the  orbit  of  Uranus. 
He  concludes  that,  if  they  be  solid  bodies  of  a  solar 
nature,  their  intrinsic  splendor  must  be  greatly  inferior 
to  that  of  the  sun,  because  a  circular  portion  of  the  sun's 
disc,  subtending  an  angle  of  20",  would  give  a  light 
equal  to  that  of  a  hundred  full  moons;  while  on  the 
contrary,  the  objects  in  question  are  hardly,  if  at  all, 
visible  to  the  naked  eye.  From  the  uniformity  of 
the  discs  of  the  planetary  nebulae,  and  their  want  of 
apparent  condensation,  he  presumes  that  they  may 


380  DISTRIBUTION  OF  THE  NEBULA.    SECT.  XXXVII 

be  hollow  shells,  only  emitting  light  from  their  sur- 
faces. 

The  existence  of  every  degree  of  ellipticity  in  the 
nebulae — from  long  lenticular  rays  to  the  exact  circular 
form — and  of  every  shade  of  central  condensation — from 
the  slightest  increase  of  density  to  apparently  a  solid 
nucleus — may  be  accounted  for  by  supposing  the  general 
constitutions  of  these  nebulae  to  be  that  of  oblate  sphe- 
roidal masses  of  every  degree  of  flatness,  from  the 
sphere  to  the  disc,  and  of  every  variety  in  their  density 
and  ellipticity  toward  the  center.  It  would  be  errone- 
ous, however,  to  imagine  that  the  forms  of  these  sys- 
tems are  maintained  by  forces  identical  with  those 
already  described,  which  determine  the  form  of  a  fluid 
mass  in  rotation ;  because,  if  the  nebulae  be  only  clus- 
ters of  separate  stars,  as  in  the  greater  number  of  cases 
there  is  every  reason  to  believe  them  to  be,  no  pressure 
can  be  propagated  through  them.  Consequently,  since 
no  general  rotation  of  such  a  system  as  one  mass  can 
be  supposed,  it  may  be  conceived  to  be  a  quiescent  form, 
comprising  within  its  limits  an  indefinite  multitude  of 
stars,  each  of  which  may  be  moving  in  an  orbit  about 
the  common  center  of  the  whole,  in  virtue  of  a  law  of 
internal  gravitation  resulting  from  the  compound  gravi- 
tation of  all  its  parts.  Sir  John  Herschel  has  proved 
that  the  existence  of  such  a  system  is  not  inconsistent 
with  the  law  of  gravitation  under  certain  conditions. 

The  distribution  of  the  nebulae  over  the  heavens  is 
even  more  irregular  than  that  of  the  stars.  In  some 
places  they  are  so  crowded  together  as  scarcely  to  allow 
one  to  pass  through  the  field  of  the  telescope  before 
another  appears,  while  in  other  parts  hours  elapse  with- 
out a  single  nebula  occurring.  They  are  in  general  only 
to  be  seen  with  the  very  best  telescopes,  and  are  most 
abundant  in  a  zone  whose  general  direction  is  not  far 
from  the  hour  circles  Oh  and  12h,  and  which  crosses  the 
milky  way  nearly  at  right  angles.  Where  that  zone 
crosses  the  constellations  Virgo,  Coma  Berenices,  and 
the  Great  Bear,  they  are  to  be  found  in  multitudes. 

Such  is  a  brief  account  of  the  discoveries  contained 
in  Sir  John  Herschel's  paper,  which,  for  sublimity  of 
views  and  patient  investigation,  has  not  been  surpassed. 


Sscr.  XXXV11.  METEORITES.  381 

To  him  and  to  Sir  William  Herschel  we  owe  almost  all 
that  is  known  of  sidereal  astronomy :  and  in  the  inimi- 
table works  of  that  highly  gifted  father  and  son,  the 
reader  will  find  this  subject  treated  of  in  a  style  alto- 
gether worthy  of  it,  and  of  them. 

Sir  John  Herschel  has  discovered  some  new  and 
wonderful  objects  in  the  southern  hemisphere.  Among 
others  a  beautiful  planetary  nebula,  having  a  perfectly 
sharp,  well  defined  disc  of  uniform  brightness,  exactly 
like  a  small  planet  with  a  satellite  near  its  edge.  Another 
is  mentioned  as  being  very  extraordinary  from  its  blue 
tint :  but  by  far  the  most  singular  is  a  close  double  star 
centrally  involve.d  in  a  nebulous  atmosphere. 

So  numerous  are  the  objects  which  meet  our  view  in 
the  heavens,  that  we  cannot  imagine  a  part  of  space 
where  some  light  would  not  strike  the  eye  ; — innumera- 
ble stars,  thousands  of  double  and  multiple  systems,  clus- 
ters in  one  blaze  with  their  tens  of  thousands  of  stars, 
and  the  nebulae  amazing  us  by  the  strangeness  of  their 
forms  and  the  incomprehensibility  of  their  nature,  till  at 
last,  from  the  limit  of  our  senses,  even  these  thin  and  airy 
phantoms  vanish  in  the  distance.  If  such  remote  bodies 
shone  by  reflected  light,  we  should  be  unconscious  of 
their  existence.  Each  star  must  then  be  a  sun,  and  may 
be  presumed  to  have  its  system  of  planets,  satellites, 
and  comets,  like  our  own ;  and,  for  aught  we  know, 
myriads  of  bodies  may  be  wandering  in  space  unseen 
by  us,  of  whose  nature  we  can  form  no  idea,  and  still 
less  of  the  part  they  perform  in  the  economy  of  the 
universe.  Even  in  our  own  system,  or  at  its  farthest 
limits,  minute  bodies  may  be  revolving  like  the  new 
planets,  which  are  so  small  that  their  masses  have  hith- 
erto been  inappreciable,  and  there  may  be  many  still 
smaller.  Nor  is  this  an  unwarranted  presumption ; 
many  such  do  come  within  the  sphere  of  the  earth's 
attraction,  are  ignited  by  the  velocity  with  which  they 
pass  through  the  atmosphere,  and  are  precipitated  with 
great  violence  on  the  earth.  The  fall  of  meteoric  stones 
is  much  more  frequent  than  is  generally  believed. 
Hardly  a  year  passes  without  some  instances  occurring ; 
and  if  it  be  considered  that  only  a  small  part  of  the  earth 
is  inhabited,  it  may  be  presumed  that  numbers  fall  in 


380  DISTRIBUTION  OF  THE  NEBULAE.    SECT.  XXXVJI 

be  hollow  shells,  only  emitting  light  from  their  sur- 
faces. 

The  existence  of  every  degree  of  ellipticity  in  the 
nebulae — from  long  lenticular  rays  to  the  exact  circular 
form — and  of  every  shade  of  central  condensation — from 
the  slightest  increase  of  density  to  apparently  a  solid 
nucleus — may  be  accounted  for  by  supposing  the  general 
constitutions  of  these  nebulae  to  be  that  of  oblate  sphe- 
roidal masses  of  every  degree  of  flatness,  from  the 
sphere  to  the  disc,  and  of  every  variety  in  their  density 
and  ellipticity  toward  the  center.  It  would  be  errone- 
ous, however,  to  imagine  that  the  forms  of  these  sys- 
tems are  maintained  by  forces  identical  with  those 
already  described,  which  determine  the  form  of  a  fluid 
mass  in  rotation ;  because,  if  the  nebula?  be  only  clus- 
ters of  separate  stars,  as  in  the  greater  number  of  cases 
there  is  every  reason  to  believe  them  to  be,  no  pressure 
can  be  propagated  through  them.  Consequently,  since 
no  general  rotation  of  such  a  system  as  one  mass  can 
be  supposed,  it  may  be  conceived  to  be  a  quiescent  form, 
comprising  within  its  limits  an  indefinite  multitude  of 
stars,  each  of  which  may  be  moving  in  an  orbit  about 
the  common  center  of  the  whole,  in  virtue  of  a  law  of 
internal  gravitation  resulting  from  the  compound  gravi- 
tation of  all  its  parts.  Sir  John  Herschel  has  proved 
that  the  existence  of  such  a  system  is  not  inconsistent 
with  the  law  of  gravitation  under  certain  conditions. 

The  distribution  of  the  nebulae  over  the  heavens  is 
even  more  irregular  than  that  of  the  stars.  In  some 
places  they  are  so  crowded  together  as  scarcely  to  allow 
one  to  pass  through  the  field  of  the  telescope  before 
another  appears,  while  in  other  parts  hours  elapse  with- 
out a  single  nebula  occurring.  They  are  in  general  only 
to  be  seen  with  the  very  best  telescopes,  and  are  most 
abundant  in  a  zone  whose  general  direction  is  not  far 
from  the  hour  circles  Oh  and  12h,  and  which  crosses  the 
milky  way  nearly  at  right  angles.  Where  that  zone 
crosses  the  constellations  Virgo,  Coma  Berenices,  and 
the  Great  Bear,  they  are  to  be  found  in  multitudes. 

Such  is  a  brief  account  of  the  discoveries  contained 
in  Sir  John  Herschel's  paper,  which,  for  sublimity  of 
views  and  patient  investigation,  has  not  been  surpassed. 


SKCT.  XXXV11.  METEORITES.  381 

To  him  and  to  Sir  William  Herschel  we  owe  almost  all 
that  is  known  of  sidereal  astronomy :  and  in  the  inimi- 
table works  of  that  highly  gifted  father  and  son,  the 
reader  will  find  this  subject  treated  of  in  a  style  alto- 
gether worthy  of  it,  and  of  them. 

Sir  John  Herschel  has  discovered  some  new  and 
wonderful  objects  in  the  southern  hemisphere.  Among 
others  a  beautiful  planetary  nebula,  having  a  perfectly 
sharp,  well  defined  disc  of  uniform  brightness,  exactly 
like  a  small  planet  with  a  satellite  near  its  edge.  Another 
is  mentioned  as  being  very  extraordinary  from  its  blue 
tint :  but  by  far  the  most  singular  is  a  close  double  star 
centrally  involved  in  a  nebulous  atmosphere. 

So  numerous  are  the  objects  which  meet  our  view  in 
the  heavens,  that  we  cannot  imagine  a  part  of  space 
where  some  light  would  not  strike  the  eye ; — innumera- 
ble stars,  thousands  of  double  and  multiple  systems,  cms-  . 
ters  in  one  blaze  with  then*  tens  of  thousands  of  stars, 
and  the  nebulae  amazing  us  by  the  strangeness  of  their 
forms  and  the  incomprehensibility  of  their  nature,  till  at 
last,  from  the  limit  of  our  senses,  even  these  thin  and  airy 
phantoms  vanish  in  the  distance.  If  such  remote  bodies 
shone  by  reflected  light,  we  should  be  unconscious  of 
their  existence.  Each  star  must  then  be  a  sun,  and  may 
be  presumed  to  have  its  system  of  planets,  satellites, 
and  comets,  like  our  own ;  and,  for  aught  we  know, 
myriads  of  bodies  may  be  wandering  in  space  unseen 
by  us,  of  whose  nature  we  can  form  no  idea,  and  still 
less  of  the  part  they  perform  in  the  economy  of  the 
universe.  Even  in  our  own  system,  or  at  its  farthest 
limits,  minute  bodies  may  be  revolving  like  the  new 
planets,  which  are  so  smaU  that  their  masses  have  hith- 
erto been  inappreciable,  and  there  may  be  many  still 
smaller.  Nor  is  this  an  unwarranted  presumption; 
many  such  do  come  within  the  sphere  of  the  earth's 
attraction,  are  ignited  by  the  velocity  with  which  they 
pass  through  the  atmosphere,  and  are  precipitated  with 
great  violence  on  the  earth.  The  fall  of  meteoric  stones 
is  much  more  frequent  than  is  generally  believed. 
Hardly  a  year  passes  without  some  instances  occurring ; 
and  if  it  be  considered  that  only  a  small  part  of  the  earth 
is  inhabited,  it  may  be  presumed  that  numbers  fall  in 


3B4  SHOOTING  STARS.  SKCT.  XXXVII. 

By  far  the  most  extraordinary  part  of  the  whole  phe- 
nomenon is  that  this  radiant  point  was  observed  to  re- 
main stationaiy  near  the  star  y  Leonis  for  more  than 
two  hours  and  a  half,  which  proved  the  source  of  the 
meteoric  shower  to  be  altogether  independent  of  the 
earth's  rotation,  and  its  parallax  showed  it  to  be  far 
above  the  atmosphere. 

As  a  body  could  not  be  actually  at  rest  in  that  posi- 
tion, the  group  or  nebula  must  either  have  been  moving 
round  the  earth  or  the  sun.  Had  it  been  moving  about 
the  earth,  the  course  of  the  meteors  would  have  been 
tangential  to  its  surface,  whereas  they  fell  almost  per- 
pendicularly, so  that  the  earth  in  its  annual  revolution 
must  have  met  with  the  group.  The  bodies  or  the 
parts  of  the  nebula  that  were  nearest  must  have  been 
attracted  toward  the  earth  by  its  gravity,  and  as  they 
were  estimated  to  move  at  the  rate  of  fourteen  miles  in 
a  second,  they  must  have  taken  fire  on  entering  our 
atmosphere,  and  been  consumed  in  their  passage  through 
it. 

As  all  the  circumstances  of  the  phenomenon  were 
similar  on  the  same  day  and  during  the  same  hours  in 
1832,  and  as  extraordinary  flights  of  shooting  stars  were 
seen  at  many  places  both  in  Europe  and  America  on 
the  13th  of  November,  1834,  1835,  and  1836,  tending 
also  from  a  fixed  point  in  the  constellation  Leo,  it  has 
been  conjectured,  with  much  apparent  probability,  that 
this  nebula  or  group  of  bodies  performs  its  revolution 
round  the  sun  in  a  period  of  about  182  days,  in  an  ellip- 
tical orbit,  whose  major  axis  is  119  millions  of  miles  ; 
and  that  its  aphelion  distance,  where  it  comes  in  contact 
with  the  earth's  atmosphere,  is  about  95  millions  of 
miles,  or  nearly  the  same  with  the  mean  distance  of 
the  earth  from  the  sun.  This  body  must  have  met 
with  disturbances  after  1799,  which  prevented  it  from 
encountering  the  earth  for  32  years,  and  it  may  again 
deviate  from  its  path  from  the  same  cause. 

As  early  as  the  year  1833,  Professor  Olmsted,  of 
Yale  College  in  the  United  States  of  America,  had  con- 
jectured that  the  phenomenon  of  shooting  stars  origi- 
nated in  the  zodiacal  light,  and  his  subsequent  observa- 
tions, continued  for  three  successive  years,  have  tended 


SECT.  XXXVIf.  SHOOTING  STARS,  385 

to  confirm  him  in  this  opinion.  He  agrees  with  La 
Place  in  thinking  that  the  zodiacal  light  is  a  nebulous 
body,  revolving  in  the  plane  of  the  solar  equator.  In 
fact,  this  light  stretches  beyond  the  earth's  orbit,  making 
an  angle  of  about  74°  with  the  plane  of  the  ecliptic,  and 
according  to  observation,  it  is  sometimes  seen  in  the 
dawn,  and  sometimes  in  the  twilight,  like  an  inferior 
planet.  It  was  seen  by  Professor  Olmsted  for  several 
weeks  previous  to  the  13th  of  November,  in  the  morn- 
ing dawn,  with  an  elongation  (N.  231)  of  from  60°  to 
90°  west  of  the  sun.  It  then  by  degrees  withdrew  from 
the  morning  sky,  and  appeared  in  the  evenings  imme- 
diately after  twilight,  rising  like  a  pyramid  through  the 
constellations  Capricornus  and  Aquarius,  to  an  elonga- 
tion of  more  than  90°  eastward  of  the  sun.  A  change 
like  this  taking  place  annually  about  the  13th  of  Novem- 
ber, has  led  the  Professor  to  believe  that  it  is  to  the 
zodiacal  light  we  are  indebted  for  those  splendid  exhibi- 
tions of  falling  stars  which  take  place  at  that  season. 

The  orbit  already  described  is  that  which  he  formerly 
assigned  to  this  nebulous  or  cometary  body,  but  he  is 
now  of  opinion  that  it  has  a  period  of  something  less 
than  a  year,  which  would  not  only  account  for  the  shoot- 
ing stare  of  the  13th  of  November,  but  would  also  ac- 
count for  those  that  happen  at  all  seasons,  and  for  some 
very  great  showers  of  them  that  have  taken  place  on 
two  occasions  near  the  end  of  April.  In  the  position 
assigned  to  this  orbit  by  Professor  Olmsted,  showers  of 
shooting  stars  may  happen  in  November  and  April. 
Since  the  last  edition  of  this  book  a  very  able  memoir 
has  been  published  by  M.  Biot,  in  which  that  great 
philosopher  shows  that  in  his  opinion  also,  meteoric 
showers  are  owing  to  the  zodiacal  light  coming  into  pe- 
riodic contact  with  the  atmosphere  of  the  earth.  Which 
of  these  conjectures  may  be  nearest  the  truth  time  alone 
can  show ;  but  certain  it  is  that  the  recurrence  of  this 
phenomenon  at  the  same  season  for  seven  successive 
years  proves  that  it  can  arise  from  no  accidental  cause. 
25  KE 


3B<5  GRAVITATING  FORCE.          SECT.  XXXVIII. 


SECTION  XXXVIII. 

Diffusion  of  Matter  through  Space — Gravitation — Its  Velocity-c Simplicity 
of  its  Laws — Gravitation  independent  of  the  Magnitude  and  Distan-es  of 
the  Bodies — Not  impeded  by  the  Intervention  of  any  Substance — Its 
Intensity  invariable — General  Laws — Recapitulation  and  Conclusion. 

THE  known  quantity  of  matter  bears  a  very  small  pro- 
portion to  the  immensity  of  space.  Large  as  the  bodies 
are,  the  distances  which  separate  them  are  immeasura- 
bly greater ;  but  as  design  is  manifest  in  every  part  of 
creation,  it  is  probable  that  if  the  various  systems  in  the 
universe  had  been  nearer  to  one  another,  their  mutual 
disturbances  would  have  been  inconsistent  with  the  har- 
mony and  stability  of  the  whole.  It  is  clear  that  space 
is  not  pervaded  by  atmospheric  air,  since  its  resistance 
would,  long  ere  this,  have  destroyed  the  velocity  of  the 
planets  ;  neither  can  we  affirm  it  to  be  a  void,  since  it 
seems  to  be  replete  with  ether,  and  traversed  in  all  di- 
rections by  light,  heat,  gravitation,  and  possibly  by  influ- 
ences whereof  we  can  form  no  idea. 

Whatever  the  laws  may  be  that  obtain  in  the  more 
distant  regions  of  creation,  we  are  assured  that  one  alone 
regulates  the  motions,  not  only  of  our  own  system,  but 
also  of  the  binary  systems  of  the  fixed  stars ;  and  as 
general  laws  form  the  ultimate  object  of  philosophical  re- 
search, we  cannot  conclude  these  remarks  without  con- 
sidering the  nature  of  gravitation— that  extraordinary 
power,  whose  effects  we  have  been  endeavoring  to  trace 
through  some  of  their  mazes.  It  was  at  one  time  im- 
agined that  the  acceleration  in  the  moon's  mean  motion 
was  occasioned  by  the ,  successive  transmission  of  the 
gravitating  force.  It  has  been  proved,  that  in  order  to 
produce  this  effect,  its  velocity  must  be  about  fifty  mill- 
ions of  times  greater  than  that  of  light,  which  flies  at 
the  rate  of  200,000  miles  in  a  second.  Its  action,  even 
at  the  distance  of  the  sun,  may  therefore  be  regarded 
as  instantaneous ;  yet  so  remote  are  the  nearest  of  the 
fixed  stars,  that  it  may  be  doubted  whether  the  sun  has 
any  sensible  influence  on  them. 

The  curves  in  which  the  celestial  bodies  move  bv  th#. 


S«cr.  XXXV1U.  GENERAL  LAWS.  387 

force  of  gravitation  are  only  lines  of  the  second  order. 
The  attraction  of  spheroids,  according  to  any  other  law 
of  force  than  that  of  gravitation,  would  be  raucji  more 
complicated  ;  and  as  it  is  easy  to  prove  that  matter  might 
have  been  moved  according  to  an  infinite  variety  of  laws, 
it  may  be  concluded  that  gravitation  must  have  been  se- 
lected by  Divine  Wisdom  out  of  an  infinity  of  others,  as 
being  the  most  simple,  and  that  which  gives  the  great- 
est stability  to  the  celestial  motions. 

It  is  a  singular  result  of  the  simplicity  of  the  laws  of 
nature,  which  admit  only  of  the  observation  and  com- 
parison of  ratios,  that  the  gravitation  and  theory  of  the 
motions  of  the  celestial  bodies  are  independent  of  their 
absolute  magnitudes  and  distances.  Consequently,  if  all 
the  bodies  of  the  solar  system,  their  mutual  distances, 
and  their  velocities,  were  to  diminish  proportionally,  they 
would  describe  curves  in  all  respects  similar  to  those  in 
which  they  now  move ;  and  the  system  might  be  suc: 
cessively  reduced  to  the  smallest  sensible  dimensions, 
and  still  exhibit  the  same  appearances.  We  learn  by 
experience  that  a  very  different  law  of  attraction  pre- 
vails when  the  particles  of  matter  are  placed  within  in- 
appreciable distances  from  each  other,  as  in  chemical 
and  capillary  attraction,  the  attraction  of  cohesion,  and 
molecular  repulsion,  yet  it  has  been  shown  that  in  all 
probability  not  only  these,  but  even  gravitation  itself,  is 
only  a  particular  case  of  the  still  more  general  principle 
of  electric  action. 

The  action  of  the  gravitating  force  is  not  impeded  by 
the  intervention  even  of  the  densest  substances.  If  the 
attraction  of  the  sun  for  the  center  of  the  earth,  and  of 
the  hemisphere  diametrically  opposite  to  him,  were  di- 
minished by  a  difficulty  in  penetrating  the  interposed 
matter,  the  tides  would  be  more  obviously  affected.  Its 
attraction  is  the  same  also,  whatever  the  substances  of 
the  celestial  bodies  may  be  ;  for  if  the  action  of  the  sun 
upon  the  earth  differed  by  a  millionth  part  from  his  ac- 
tion upon  the  moon,  the  difference  would  occasion,  a 
periodical  variation  in  the  moon's  parallax,  whose  maxi- 
mum would  be  the  Tj  of  a  second,  and  also  a  variation  in 
her  longitude  amounting  to  several  seconds,  a  supposi- 
tion proved  to  be  impossible,  by  the  agreement  of  theory 


388  GRAVITATING  FORCE.  SECT.  XXXVIII. 

with  observation.  Thus  all  matter  is  pervious  to  gravi- 
tation, and  is  equally  attracted  by  it. 

Gravitation  is  a  feeble  force,  vastly  inferior  to  electric 
action,  chemical  affinity,  and  cohesion  ;  yet  as  far  as 
human  knowledge  extends,  the  intensity  of  gravitation 
has  never  varied  within  the  limits  of  the  solar  system ; 
nor  does  even  analogy  lead  us  to  expect  that  it  should  : 
on  the  contrary,  there  is  every  reason  to  be  assured  that 
the  great  laws  of  the  universe  are  immutable,  like  their 
Author.  Not  only  the  sun  and  planets,  but  the  mi- 
nutest particles,  in  all  the  varieties  of  their  attractions 
and  repulsions, — nay,  even  the  imponderable  matter  of  the 
electric,  galvanic,  or  magnetic  fluid,- — are  all  obedient  to 
permanent  laws,  though  we  may  not  be  able  in  every  case 
to  resolve  their  phenomena  into  general  principles.  Nor 
can  we  suppose  the  structure  of  the  globe  alone  to  be 
exempt  from  the  universal  fiat,  though  ages  may  pass 
before  the  changes  it  has  undergone,  or  that  are  now  in 
progress,  can  be  referred  to  existing  causes  with  the 
same  certainty  with  which  the  motions  of  the  planets, 
and  all  their  periodic  and  secular  variations,  are  refera- 
ble to  the  law  of  gravitation.  The  traces  of  extreme 
antiquity  perpetually  occurring  to  the  geologist  give  that 
information,  as  to  the  origin  of  things,  in  vain  looked  for 
in  the  other  parts  of  the  universe.  They  date  the  be- 
ginning of  time  with  regard  to  our  system  ;  since  there 
is  ground  to  believe  that  the  formation  of  the  earth  was 
contemporaneous  with  that  of  the  rest  of  the  planets ; 
but  they  show  that  creation  is  the  work  of  Him  with 
whom  "  a  thousand  years  are  as  one  day,  and  one  day 
as  a  thousand  years." 

In  the  work  now  brought  to  a  conclusion,  it  has  been 
necessary  to  select  from  the  whole  circle  of  the  sciences 
a  few  of  the  most  obvious  of  those  proximate  links  which 
connect  them  together,  and  to  pass  over  innumerable 
cases  both  of  evident  and  occult  alliance.  Any  one 
branch  traced  through  its  ramifications  would  alone  have 
occupied  a  volume ;  it  is  hoped,  nevertheless,  that  the 
view  here  given  will  suffice  to  show  the  extent  to  which 
a  consideration  of  the  reciprocal  influence  of  even  a  few 
of  these  subjects  may  ultimately  lead.  It  thus  appears 
thnt  the  theory  of  dynamics,  founded  upon  terrestrial 


S«cr.  XXXVIII.  CONCLUSIUX.  389 

pheuomenH,  is  indispensable  for  acquiring  a  knowledge 
of  the  revolutions  of  the  celestial  bodies  and  their  recip- 
rocal influences.  The  motions  of  the  satellites  are  af- 
fected by  the  forms  of  their  primaries,  and  the  figures 
of  -the  planets  themselves  depend  upon  their  rotations. 
The  symmetry  of  their  internal  structure  proves  the 
stability  of  these  rotatory  motions,  and  the  immutability 
of  the  length  of  the  day,  which  furnishes  an  invariable 
standard  of  time ;  and  the  actual  size  of  the  terrestrial 
spheroid  affords  the  means  of  ascertaining  the  dimensions 
of  the  solar  system,  and  provides  an  invariable  founda- 
tion for  a  system  of  weights  and  measures.  The  mutual 
attraction  of  the  celestial  bodies  disturbs  the  fluids  at 
their  surfaces,  whence  the  theory  of  the  tides  and  of  the 
oscillations  of  the  atmosphere.  The  density  and  elas- 
ticity of  the  air,  varying  with  every  alternation  of  tern-' 
perature,  lead  to  the  consideration  of  barometrical 
changes,  the  measurement  of  heights,  and  capillary  at- 
traction ;  and  the  doctrine  of  sound,  including  the  theory 
of  music,  is  to  be  referred  to  the  small  undulations  of 
the  aerial  medium.  A  knowledge  of  the  action  of  mat- 
ter upon  light  is  requisite  for  tracing  the  curved  path  of 
its  rays  through  the  atmosphere,  by  which  the  true 
places  of  distant  objects  are  determined  whether  in  the 
heavens  or  on  the  earth.  By  this  we  learn  the  nature 
and  properties  of  the  sunbeam,  the  mode  of  its  propaga- 
tion through  the  ethereal  fluid,  or  in  the  interior  of  ma- 
terial bodies,  and  the  origin  of  color.  By  the  eclipses  of 
Jupiter's  satellites,  the  velocity  of  light  is  ascertained ;  and 
that  velocity,  in  the  aberration  of  the  fixed  stars,  fur- 
nishes the  only  direct  proof  of  the  real  motion  of  the 
earth.  The  effects  of  the  invisible  rays  of  light  are  im- 
mediately connected  with  chemical  action ;  and  heat, 
forming  a  part  of  the  solar  ray  so  essential  to  animated 
and  inanimated  existence,  whether  considered  as  invisi- 
ble light  or  as  a  distinct  quality,  is  too  important  an  agent 
in  the  economy  of  creation,  not  to  hold  a  principal  place 
in  the  connection  of  physical  sciences.  Whence  follows 
its  distribution  in  the  interior  and  over  the  surface  of  the 
globe,  its  power  on  the  geological  convulsions  of  our 
planet,  its  influence  on  the  atmosphere  and  on  climate, 
and  its  effects  on  vegetable  and  animal  life,  evinced  in 
K  K  2 


390  CONCLUSION.  SKCT.  XXXV1U. 

the  localities  of  organized  beings  on  the  earth,  in  the 
waters,  and  in  the  air.  The  connection  of  heat  with 
electrical  phenomena,  and  the  electricity  of  the  atmos- 
phere, together  with  all  its  energetic  effects,  its  identity 
with  magnetism  and  the  phenomena  of  terrestrial  po- 
larity, can  only  be  understood  from  the  theories  of  these 
invisible  agents,  and  are,  probably,  identical  with,  or  at 
least  the  principal  causes  of,  chemical  affinities.  Innu- 
merable instances  might  be  given  in  illustration  of  the 
immediate  connection  of  the  physical  sciences,  most  of 
which  are  united  still  more  closely  by  the  common  bond 
of  analysis,  which  is  daily  extending  its  empire,  and  will 
ultimately  embrace  almost  every  subject  in  nature  in  its 
formulae. 

These  formulae,  emblematic  of  Omniscience,  condense 
into  a  few  symbols  the  immutable  laws  of  the  universe. 
This  mighty  instrument  of  human  power  itself  originates 
in  the  primitive  constitution  of  the  human  mind,  and 
rests  upon  a  few  fundamental  axioms,  which  have  eter- 
nally existed  in  Him  who  implanted  them  in  the  breast 
of  man  when  He  created  him  after  His  own  image. 


NOTE  S. 


NOTE  1^  page  2. — Diameter.  A  straight  line  passing  through  the  cen- 
ter, and  terminated  both  ways  by  the  sides  or  surface  of  a  figure,  such  as 
of  a  circle  or  sphere.  In  fig.  1,  q  (J,  N  S,  are  diameters. 

NOTE  2,  p.  2. — Mathematical  and  mechanical  sciences.  Mathematics 
leach  the  laws  of  number  and  quantity ;  mechanics  treat  of  the  equi- 
librium and  motion  of  bodies. 

NOTE  3,  p.  2. — .Analysis  is  a  series  of  reasoning  conducted  by  signs  or 
symbols  of  the  quantities  whose  relations  form  the  subject  of  inquiry. 

NOTE  4,  p.  3. — Oscillations  are  movements  to  and  fro,  like  the  swing- 
ing of  the  pendulum  of  a  clock,  or  waves  in  water.  The  tides  are  oscil- 
lations of  the  sea. 

NOTE  5,  p.  3.— Gravitation.  Gravity  is  the  reciprocal  attraction  of 
matter  on  matter  ;  gravitation  is  the  difference  between  gravity  and  the 
centrifugal  force  induced  by  the  velocity  of  rotation  or  revolution.  Sen- 
sible gravity,  or  weight,  is  a  particular  instance  of  gravitation.  It  is  the 
force  which  causes  substances  to  fall  to  the  surface  of  the  earth,  and 
which  retains  the  celestial  bodies  in  their  orbits.  Its  intensity  increases 
as  the  squares  of  the  distance  decrease. 

NOTE  6,  p.  4.— Particles  of  matter  are  the  indefinitely  small  or  ultimate 
atoms  into  which  matter  is  believed  to  be  divisible.  Their  form  is  un- 
known ;  but  though  too  small  to  be  visible,  they  must  have  magnitude.. 

NOTE  7,  p.  4.— J  hollow  sphere.  A  hollow  ball^  like  a  bomb-shell.  A 
sphere  is  a  ball  or  solid  body,  such,  that  all  lines  drawn  from  its  center 
to-  its  surface  are  equal.  They  are  palled  radii,  and  every  line  passing 
through  the  center  and  terminated  both  ways  by  the  surface  is  a  diameter, 
which  is  consequently  equal  to  twice  the  radius.  In  fig.  3,  Q  q  or  N  S  is 
a  diameter,  and  C  Q,  C  N  are  radii.  A  great  circle  of  the  sphere  has  the 
same  center  with  the  sphere  as  the  circles  QEqd  and  Q. N  q 3.  The 
circle  A  B  is  a  lesser  circle  of  the  sphere. 

NOTE  8,  p.  4. — Concentric  hollow  spheres.  Shells,  or  hollow  spheres, 
having  the  same  center,  like  the  coats  of  an  onion. 

NOTE  9,  p.  4.— Spheroid.   A  solid  body,  which  sometimes  has  the  shape 


Fi<r.  I. 


392 


AOTEri. 


of  an  orange,  as  m  fig.  1 ;  it  is  then  called  an  oblate  spheroid,  because  it 
is  flattened  at  the  poles  N  and  S.  Such 
is  the  form  of  the  earth  and  planets. 
When,  on  the  contrary,  it  is  drawn  out 
of  the  poles  like  an  egg,  as  in  fig.  2,  it  is 
called  a  prolate  spheroid.  It  is  evident 
that  in  both  these  solids  the  radii  C  g,  C  a, 
CN,  &c.,  are  generally  unequal ;  where- 
as in  the  sphere  they  are  all  equal. 

NOTE  10,  p.  4, — Center  of  gravity.  A 
point  in  every  body,  which  if  supported, 
the  body  will  remain  at  rest  in  what-  2 
ever  position  it  may  be  placed.  About 
that  point  all  the  parts  exactly  balance 
one  another.  The  celestial  bodies  at- 
tract each  other  as  if  each  were  con- 
densed into  a  single  particle  situate  in 
the  center  of  gravity,  or  the  particle  situ- 
ate in  the  center  of  gravity  of  each  may 
be  regarded  as  possessing  the  resultant 
power  of  the  innumerable  oblique  forces  which  constitute  the  whole 
attraction  of  the  body. 

NOTE  11,  pp.  4,  G. — Poles  and  equator.  Let  fig.  1  or  3  represent  the 
earth,  C  its  center,  NCS  the  axis  of  rotation,  or  the  imaginary  line  about 
which  it  performs  its  daily  revolution.  Then  N  and  S  are  the  north  and 
south  poles,  and  the  great  circle  q  E  Q,  which  divides  the  earth  into  two 
equal  parts,  is  the  equator.  The 
earth  is  flattened  at  the  poles  fig. 
1,  the  equatorial  diameter,  g  Q, 
exceeding  the  polar  diameter,  N  S, 
by  about  26£  miles.  Lesser  cir- 
cles, A  B  G,  which  are  parallel  to 
the  equator,  are  circles  or  parallels 
of  latitude,  which  is  estimated  in 
degrees,  minutes,  and  seconds, 
north  and  south  of  the  equator, 
every  place  in  the  same  parallel 
having  the  same  latitude  :  Green- 
wich is  in  the  parallel  of  51°28'40". 
Thus  terrestrial  latitude  is  the  an- 
gular distance  between  the  direc- 
tion of  a  plumb-line  at  any  place 
and  the  plane  of  the  equator. 
Lines  such  as  NClS,  NGES, 
fig.  3,  are  called  meridians ;  all  the  places  in  any  one  of  these  lines  have 
noon  at  the  same  instant.  The  meridian  of  Greenwich  has  been  chosen 
by  the  British  as  the  origin  of  terrestrial  longitude,  which  is  estimated  in 
degrees,  minutes,  and  seconds,  east  and  west  of  that  line.  If  N  G  E  S  be 
the  meridian  of  Greenwich,  the  position  of  any  place,  B,  is  determined, 
when  its  latitude,  Q,CB,  and  its  longitude,  EC  Q,  are  known. 

NOTE  12,  p.  4. — Mean  quantities  are  such  as  are  intermediate  between 
others  that  are  greater  and  less.  The  mean  of  any  number  of  unequal 
quantities  is  equal  to  their  sum  divided  by  their  number.  For  instance, 
the  mean  between  two  unequal  quantities'is  equal  to  half  their  sum. 

NOTE  13,  p.  4. — Ji  certain  mean  latitude.  The  attraction  of  a  sphere  on 
an  external  body  is  the  same  as  if  its  mass  were  collected  into  one  heavy 
particle  in  its  center  of  gravity,  and  the  intensity  of  its  attraction  dimin- 
ishes as  the  square  of  its  distance  from  the  external  body  increases.  But 


NOTES. 


393 


the  attraction  of  a  spheroid,  fig.  1,  on  an  external  body  at  m  in  the  plane 
of  its  equator,  E  Q,,  is  greater,  and  its  attraction  on  the  same  body  when 
at  m'  in  tiie  axis  X  S  less,  than  if  it  were  a  sphere.  Therefore,  in  both 
cases,  the  Ibrce  deviates  from  the  exact  law  of  gravity.  This  deviation 
arises  from  the  protuberant  matter  at  the  equator ;  and  as  it  diminishes 
toward  the  poles,  so  does  the  attractive  force  of  the  spheroid.  But  there 
is  one  mean  latitude,  where  the  attraction  of  a  spheroid  is  the  same  as 
if  it  were  a  sphere.  It  is  a  part  of  the  spheroid  intermediate  between  the 
equator  and  the  pole.  In  that  latitude  the  square  of  the  sine  is  equal  to 
£  of  the  equatorial  radius. 

NOTE  14,  p.  4. — Mean  distance..  The  mean  distance  of  a  planet  from 
the  center  of  the  sun,  or  of  a  satellite  from  the  center  of  its  planet,  is 
equal  to  half  the  sum  of  its  greatest  and  least  distances,  and  consequently 
is  equal  to  half  the  major  axis  of  its  orbit.  For  example,  let  PQ,  A  D, 
fig.  6,  be  the  orbit  or  path  of  the  moon  or  of  a  planet ;  then  P  A  is  the 
major  axis,  C  the  center,  and  CS  is  equal  to  CF.  Now,  since  the  earth 
or  the  sun  is  supposed  to  be  in  the  point  S  according  as  P  D  A  Q,  is  regarded 
as  the  orbit  of  the  moon  or  that  of  a  planet,  S  A,  S  P  are  the  greatest  and 
least  distances.  But  half  the  sum  of  S  A  and  S  P  is  equal  to  half  of  A  P, 
the  major  axis  of  the  orbit.  When  the  body  is  at  Q.  or  D,  it  is  at  its 
mean  distance  from  S,  for  S  <i,  S  D  are  each  equal  to  C  P,  half  the  major 
axis  by  the  nature  of  the  curve. 

NOTE  15,  p.  4. — Mean  radius  of  the  earth.  The  distance  from  the  cen- 
ter to  the  surface  of  the  earth,  regarded  aa  a  sphere.  It  is  intermediate 
between  the  distances  of  the  center  of  the  earth  from  the  pole  and  from 
the  equator. 

NOTE  16,  p.  5. — Ratio.  The  relation  which  one  quantity  bears  to 
another. 

NOTE  17,  p.  5. — Square  of  moon's  distance.  In  order  to  avoid  large 
numbers,  the  mean  radius  of  the  earth  is  taken  for  unity :  then  the  mean 
distance  of  the  moon  is  expressed  by  60 ;  and  the  square  of  that  number 
is  3600,  or  60  tunes  60. 

NOTE  18,  p.  5.— Centrifugal  force.  The  force  with  which  a  revolving 
body  tends  to  fly  from  the  center  of  motion  :  a  sling 'tends  to  fly  from  the 
hand  in  consequence  of  the  centrifugal  force.  A  tangent  is  a  straight  line 
touching  a  curved  line  in  one  point  without  cutting  it,  as  mT,  fig.  4.  The 
direction  of  the  centrifugal  force  is 
in  the  tangent  to  the  curved  line  or 
path  in  which  the  body  revolves, 
and  its  intensity  increases  with  the 
angular  swing  of  the  body,  and  with, 
its  distance  from  the  center  of  mo- 
tion. As  the  orbit  of  the  moon  does 
not  differ  much  from  a  circle,  let  it 
be  represented  by  m  dg  h,  fig.  4, 
the  earth  being  in  C.  The  centri- 
fugal  force  arising  from  the  velocity 
of  the  moon  in  her  orbit  balances 
the  attraction  of  the  earth.  By  their 
joint  action, the  moon  moves  through 
the  arc  m  n  during  the  time  that  she 
would  fly  off  in  the  tangent  mT  by 
the  action  of  the  centrifugal  force 
atone,  or  fall  through  mp  by  the 
earth's  attraction  alone.  T  n,  the 
deflection  from  the  tangent,  is  parallel  and  equal  to  mp,  the  versed  sine 
of  the  arc  m  n,  supposed  to  be  moved  over  by  the  moon  in  a  second,  and 
therefore  so  very  small  that  it  may  be  regarded  as  a  straight  line.  T  w, 


394 


NOTES. 


or  mp,  is  the  space  the  iwoon  would  fall  through  in  the  first  second  of 
her  descent  to  the  earth,  were  she  not  retained  in  her  orbit  by  her  cen- 
trifugal force. 

NOTE  19,  p.  5. — Action  and  reaction.  When  motion  is  communicated 
by  collision  or  pressure,  the  action  of  the  body  which  strikes  is  returned 
with  equal  force  by  the  body  which  receives  the  blow.  The  pressure  of 
a  hand  on  a  table  is  resisted  with  an  equal  and  contrary  force.  This 
necessarily  follows  from  the  impenetrability  of  matter,  a  property  by  which 
no  two  particles  of  matter  can  occupy  the  same  identical  portion  of  space 
at  the  same  time.  When  motion  is  communicated  without  apparent 
contact,  as  in  gravitation,  attraction,  and  repulsion,  the  quantity  of  motion 
gained  by  the  one  body  is  exactly  equal  to  that  lost  by  the  other,  but  in  a, 
contrary  direction  ;  a  circumstance  known  by  experience  only. 

NOTE  20,  p.  5. — Projected.  A  body  is  projected  when  it  is  thrown  ;  u 
ball  fired  from  a  gun  is  projected  ;  it  is  therefore  called  a  projectile.  But 
the  word  has  also  another  meaning.  A  line,  surface,  or  solid  body,  is 
said  to  be  projected  upon  a  plane,  when  parallel  straight  lines  are  drawn 
from  every  point  of  it  to  the  plane.  The  figure  so  traced  upon  the  plane 
is  a  projection.  The  projection  of  a  terrestrial  object  is  therefore  its  day- 
light shadow,  since  the  sun's  rays  are  sensibly  parallel. 

NOTE  21 ,  p.  5. — Space.  The  boundless  region  which  contains  all  creation. 

NOTE  22,  pp.  5,  12. — Conic  Sections.    Lines  formed  by  any  plane  cut- 


Fig.  6. 


Fig.l. 


Fig.  8. 


NOTES.  395 

ting  a  cone.  A  cone  is  a  solid  figure,  like  a  sugar-loaf,  fig.  5,  of  which  A 
is  the  apex,  AD  the  axis,  and  the  plane  BECF  the  base.  The  axis 
may  or  may  not  be  perpendicular  to  the  base,  and  the  base  may  be  a 
circle,  or  any  other  curved  line.  When  the  axis  is  perpendicular  to  the 
base,  the  solid  is  a  right  cone.  If  a  right  cone  with  a  circular  base  be  cut 
at  ri-jlit  a'ngles  to  the  base  by  a  plane  passing  through  the  apex,  the  sec- 
tion will  be  a  triangle.  If  the  cone  be  cut  through  both  sides  by  a  plane 
parallel  to  the  base,  the  section  will  be  a  circle.  If  the  cone  be  cut  slanting 
quite  through  both  sides,  the  section  will  be  an  ellipse,  fig.  6.  If  the  cone 
be  cut  parallel  to  one  of  the  sloping  sides,  as  A  B,  the  section  will  be  a 
parabola,  fig.  7.  And  if  the  plane  cut  only  one  side  of  the  cone,  and  be  not 
parallel  to  the  other,  the  section  will  be  a  hyperbola,  fig.  8.  Thus  there 
are  five  conic  sections. 

NOTE  23,  p.  5. — Inverse  square  of  distance.  The  attraction  of  one  body 
for  another  at  the  distance  of  two  miles  is  four  times  less  than  at  the 
distance  of  one  mile ;  at  three  miles,  it  is  nine  times  less  than  at  one ;  at 
four  miles,  it  is  sixteen  times  less,  and  so  on.  That  is,  the  gravitating 
force  decreases  in  intensity  as  the  squares  of  the  distance  increase. 

NOTE  24,  p.  5. — Ellipse.  One  of  the  conic  sections,  fig.  6.  An  ellipse 
may  be  drawn  by  fixing  the  ends  of  a  string  to  two  points,  S  and  F,  in  a 
sheet  of  paper,  and  then  carrying  the  point  of  a  pencil  round  in  the  loop 
of  the  string  kept  stretched,  the  length  of  the  strkig  being  greater  than 
the  distance  between  the  two  points.  The  points  S  and  F  are  called  the 
foci,  C  the  center,  SC  or  CF  the  eccentricity,  A  P  the  major  axis,  QD 
the  minor  axis,  and  P  S  the  focal  distance.  It  is  evident  that  the  less  the 
eccentricity  CS,  the  nearer  does  the  ellipse  approach  to  a  circle;  and 
from  the  construction  it  is  clear  that  the  length  of  the  string  SmF.is 
equal  to  the  major  axis  PA.  If  T  t  be  a  tangent  to  the  ellipse  at  TO,  then 
the  angle  TmS  is  equal  to  the  angle  t mF;  and  as  this  is  true  for  every 
point  in  the  ellipse,  it  follows,  that  in  an  elliptical  reflecting  surface,  rays 
of  light  or  sound  coming  from  one  focus  S  will  be  reflected  by  the  surface 
to  the  other  focus  F,  since  the  angle  of  incidence  is  equal  to" the  angle  of 
reflection  by  the  theories  of  light  and  sound. 

NOTE  25,  p.  5. — Periodic  time.  The  time  in  which  a  planet  or  comet 
performs  a  revolution  round  the  sun,  or  a  satellite  about  its  planet. 

NOTE  26,  p.  5.  Kepler  discovered  three  laws  in  the  planetary  motions 
by  which  the  principle  of  gravitation  is  established :— 1st  law,  That  the 
radii  vectores  of  the  planets  and  comets  describe  areas  proportional  to  the 
time.  Let  fig.  9  be  the  orbit  of  a  planet ;  Fig.  9. 

then  supposing  the  spaces  or  areas  PSp, 
p  S  a,  aSb,  &c.  equal  to  one  another,  the 
radius  vector  S  P,  which  is  the  line  joining 
the  centers  of  the  sun  and  planet,  passes 
over  these  equal  spaces  in  equal  times, 
that  Is,  if  the  line  S  P  passes  to  Sp  in  one  p 
day,  it  wHl  come  to  So  in  two  days,  to  S b 
in  three  days,  and  so  on.  2d  law,  That  the 
orbits  or  paths  of  the  planets  and  comets 
are  conic  sections,  having  the  sun  in  one  of 
their  foci.  The  orbits  of  the  planets  and 
satellites  are  curves  like  fig.  6  or  9,  called 
ellipses,  having  the  sun  in  the  focus  8.  Three  comets  are  known  to 
move  in  ellipses,  but  the  greater  part  seem  to  move  in  parabolas,  fig.  7, 
having  the  sun  in  S,  though  it  is  probable  that  they  really  move  in  very 
long  flat  ellipses;  others  appear  to  move  in  hyperbolas,  like  fig.  8.  The 
third  law  is,  that  the  squares  of  the  periodic  times  of  the  planets  are  pro- 
portional to  the  cubes  of  their  mean  distances  from  the  sun.  The  square 
of  a  number  is  that  number  multiplied  by  itself,  and  the  cube  of  a  mnu 


396  NOTES. 

ber  is  that  number  twice  multiplied  by  itself.  For  example,  the  squares 
of  the  numbers  2,  3,  4,  &c.  are  4,  9,  16,  &c.,  but  their  cubes  are  8,  27,  64, 
&c.  Then  the  squares  of  the  numbers  representing  the  periodic  times  of 
two  planets  are  to  one  another  as  the  cubes  of  the  numbers  representing 
their  mean  distances  from  the  sun.  So  that  throe  of  these  quantities 
being  known,  the  other  may  be  found  by  the  rule  of  three.  The  mean 
distances  are  measured  in  miles  or  terrestrial  radii,  and  the  periodic  times 
are  estimated  in  years,  days,  and  parts  of  a  day.  Kepler's  laws  extend  to 
the  satellites. 

NOTE  27,  p.  5. — Mass.  The  quantity  of  matter  in  a  given  bulk.  It  is 
proportional  to  the  density  and  volume  or  bulk  conjointly. 

NOTE  28,  p.  5. —  Gravitation  proportional  to  mass.  But  for  the  resist- 
ance of  the  air,  all  bodies  would  fall  to  the  ground  in  equal  times.  In 
fact  a  hundred  equal  particles  of  matter  at  equal  distances  from  the  sur- 
face of  the  earth  would  fall  to  the  ground  in  parallel  straight  lines  with 
equal  rapidity,  and  no  change  whatever  would  take  place  in  the  circum- 
stances of  their  descent,  if  99  of  them  were  united  in  one  solid  mass;  for 
the  solid  mass  and  the  single  particle  would  touch  the  ground  at  the 
same  instant,  were  it  not  for  the  resistance  of  the  air. 

NOTE  29,  p.  5. — Primary  signifies,  in  astronomy,  the  planet  about  which 
a  satellite  revolves.  The  earth  is  primary  to  the  moon. 

NOTE  30,  p.  6.— Rotation.     Motion  round  an  axis,  real  or  imaginary. 

NOTE  31,  p.  7. —  Compression  of  a  spheroid.  The  flattening  at  the  poles. 
It  is  equal  to  the  difference  between  the  greatest  and  least  diameters, 
divided  by  the  greatest ;  these  quantities  being  expressed  in  some  stand- 
ard measure,  as  miles. 

NOTE  32,  p.  7. — Satellites.  Small  bodies  revolving  about  some  of  the 
plane'ts.  The  moon  is  a  satellite  to  the  earth. 

NOTE  33,  p.  7. — Nutation.  A  nodding  motion  in  the  earth's  axis  while 
in  rotation,  similar  to  that  observed  in  the  spinning  of  a  top.  It  is  pro- 
duced by  the  attraction  of  the  sun  and  moon  on  the  protuberant  matter 
at  the  terrestrial  equator. 

NOTE  34,  p.  l.—Jlxis  of  Rotation.  The  line,  real  or  imaginary,  about 
which  a  body  revolves.  The  axis  of  the  earth's  rotation  is  that  diameter, 
or  imaginary  line,  passing  through  the  center  and  both  poles.  Fig.  1  being 
the  earth,  N  S  is  the  axis  of  rotation. 

NOTE  35,  p.  7. — Nutation  of  lunar  orbit.  The  action  of  the  bulging 
matter  at  the  earth's  equator  on  the  moon  occasions  a  variation  in  the 
inclination  of  the  lunar  orbit  to  the  plane  of  the  ecliptic.  Suppose  the 
plane  Np  n,  fig.  13,  to  be  the  orbit  of  the  moon,  and  N  m  n  the  plane  of  the 
ecliptic,  the  earth's  action  on  the  moon  causes  the  angle  pNwi  to  become 
less  or  greater  than  its  mean  state.  The  nutation  in  the  lunar  orbit  is  the 
reaction  of  the  nutation  in  the  earth's  axis. 

NOTE  3G,  p.  7 .—  Translated.    Carried  forward  in  space. 

NOTE  37,  p.  8. — Force  proportional  to  velocity.  Since  a  force  is  meas- 
ured by  its  effect,  the  motions  of  the  bodies  of  the  solar  system  among 
themselves  would  be  the  same  whether  the  system  be  at  rest  or  not.  The 
real  motion  of  a  person  walking  the  deck  of  a  ship  at  sea  is  compounded 
of  his  own  motion  and  that  of  the  ship,  yet  each  takes  place  independently 
of  the  other.  We  walk  about  as  if  the  earth  were  at  rest,  though  it  has 
the  double  motion  of  rotation  on  its  axis  and  revolution  round  the  sun. 

NOTE  38,  p.  8. —  Tangent,  A  straight  line  which  touches  a  curved 
line  in  one  point  without  cutting  it.  In  fig.  4,  m  T  is  tangent  to  the  curve 
in  the  point  m.  In  a  circle  the  tangent  is  at  right  angles  to  the  radius  C  m. 

NOTE  39,  p.  8. — Motion  in  an  elliptical  orbit.  A  planet  m,  fig.  6,  moves 
round  the  sun  at  S  in  an  ellipse  P  D  A  Q,  in  consequence  of  two  forces 


NOTES. 


397 


one  urging  it  in  the  direction  of  the  tangent  mT,  and  another  pulling  it 
toward  the  sun  in  the  direction  mS.  Its  velocity,  which  is  greatest  at 
P.  decreases  throughout  the  arc  to  P  D  A  to  A,  where  it  is  least,  and 
increases  continually  as  it  moves  along  the  arc  A  Q,P  till  it  comes  to  P 
again.  The  whole  force  producing  the  elliptical  motion  varies  inversely 
as  the  square  of  the  distance.  See  Note  23. 

NOTE  40,  p.  8. — Radii  vectores.  Imaginary  lines  joining  the  center  of 
the  sun  and  the  center  of  a  planet  or  comet,  or  the  centers  of  a  planet  and 
its  satellite.  In  the  circle,  the  radii  are  all  equal  ;  but  in  an  ellipse,  fig.  6, 
the  radius  vector  SA  is  greater,  and  SP  less  than  ail  the  others.  The 
r;idii  vectores,  S  Q,  S  D,  are  equal  to  C  A  or  C  P,  half  the  major  axis  P  A, 
and  consequently  equal  to  the  mean  distance.  A  planet  is  at  its  mean 
distance  from  the  sun  when  in  the  points  Q,  and  D. 

NOTE  41,  p.  8.— Equal  areas  in  equal  times.  See  Kepler's  1st  law  in 
Note  -26.  p.  5. 

NOTE  42,  p.  8.— Major  Axis..  The  line  P  A,  fig.  6  or  10. 

NOTE  43,  p.  9.— If  the  planet  de-  J*^  Fig.  10. 

scribed  a  circle,  S,-c.  The  motion  of 
a  planet  about  the  eun,  in  a  cirele 
A  B  P.  fig.  10,  whose  radius  C  A  is 
equal  to  the  planet's  mean  distance 
from  him,  would  be  equable,  that 
is,  its  velocity,  or  speed,  would  al- 
ways be  the  same.  Whereas,  if  it 
moved  in  the  ellipse  A  Q.  P.  its 
speed  would  be  continually  vary- 
ing, by  Note  39 ;  but  its  motion  is 
such,  that  the  time  elapsing  be- 
tween its  departure  from  P,  and  its 


return  to  that  point  agaiq,  would  be 
the  same,  whether  it  moved  in  the 
circle  or  in  the  ellipse  ;  for  these 
curves  coincide  in  the  points  P  &  A. 

NOTE  44,  p.  9. — True  motion.  The  motion  of  a  body  in  its  real  orbit 
PDA  a,  fig.  10. 

NOTE  45,  p.  9.— -Vean  motion.  Equable  motion  in  a  circle  P  E  A  B, 
fig.  10,  at  the  mean  distance  C  P  or  C  m,  in  the  time  that  the  body  would 
accomplish  a  revolution  in  its  elliptical  orbit  P  D  A  Q,. 


NOTE  46,  p.  9.  —  The  equi- 
nox. Fig.  11  represents  the 
celestial  sphere,  and  G  its 
center,  where  the  earth  is  sup- 
posed to  be.  q  T  Q  ^=  is  the 
equinoctial  or  great  circle, 
traced  in  the  starry  heavens 
by  an  imaginary  extension  of 
the  plane  of  the  terrestrial 
equator,  and  E  T  e  =£=  is  the 
ecliptic,  or  apparent  path  of " 
the  sun  round  the  earth.  T  :£=, 
the  intersection  of  these  two 
planes,  is  the  line  of  the  equi- 
noxes ;  T  is  the  vernal  equi- 
nox, and  =£=  the  autumnal. 
When  the  sun  i.s  in  these 
points,  the  days  and  nights 
are  equal.  They  are  distant 
from  one  another  by  a  aetni- 


Fig.  11. 


398  NOTES. 

circle,  or  two  right  angles.  The  points  E  and  e  are  the  solstices, 
where  the  sun  is  at  his  greatest  distance  from  the  equinoctial. 
The  equinoctial  is  everywhere  ninety  degrees  distant  from  its  poles 
N  and  S,  which  are  two  points  diametrically  opposite  to  one  another, 
where  the  axis  of  the  earth's  rotation,  if  prolonged,  would  meet  the 
heavens.  The  northern  celestial  pole  N  is  within  1°  24'  of  the  pole 
star.  As  the  latitude  of  any  place  on  the  surface  of  the  earth  is  equal  to 
the  height  of  the  pole  above  the  horizon,  it  is  easily  determined  by 
observation.  The  ecliptic  E  T  e  ^±  is  also  everywhere  ninety  degrees 
distant  from  its  poles  P  and  p.  The  angle  P  C  N,  between  the  poles  P 
and  N  of  the  equinectial  and  ecliptic,  is  equal  to  the  angle  e  C  Q.,  called 
the  obliquity  of  the  ecliptic. 

NOTE  47,  p.  $.— Longitude.  The  vernal  equinox,  T,  fig.  11,  is  the 
zero  point  in  the  heavens  whence  celestial  longitudes,  or  the  angular 
motions  of  the  celestial  bodies,  are  estimated  from  west  to  east,  the 
direction  in  which  they  all  revolve.  The  vernal  equinox  is  generally 
called  the  first  point  of  Aries,  though  these  two  points  have  not  coin- 
cided since  the  early  ages  of  astronomy,  about  2233  years  ago,  on  account 
of  a  motion  in  the  equinoctial  points,  to  be  explained  hereafter.  If  S  T, 
fig.  10,  be  the  line  of  the  equinoxes,  and  T  the  vernal  equinox,  the  true 
longitude  of  a  planet  p  is  the  angle  T  Sp,  and  its  mean  longitude  is  the 
angle  T  C  m,  the  sun  being  in  S.  Celestial  longitude  is  the  angular 
distance  of  a  heavenly  body  from  the  vernal  equinox  ;  whereas  terres- 
trial longitude  is  the  angular  distance  of  a  place  on  the  surface  of  the 
earth  from  a  meridian  arbitrarily  chosen,  as  that  of  Greenwich. 

NOTE  48,  pp.  9,  57. — Equation  of  the  center.  The  difference  between 
T  Cm  and  T  Sp,  fig.  10;  that  is,  the  difference  between  the  true  and 
mean  longitudes  of  a  planet  or  satellite.  The  true  and  mean  places  only 
coincide  in  the  points  P  and  A ;  in  every  other  point  of  the  orbit,  the 
true  place  is  either  before  or  behind  the  mean  place.  In  moving  from  A 
through  the  arc  A  Q.  P,  the  true  place  p  is  behind  the  mean  place  m ; 
and  through  the  arc  PDA  the  true  place  is  before  the  mean  place.  At 
its  maximum,  the  equation  of  the  center  measures  C  S,  the  eccentricity 
of  the  orbit,  since  it  is  the  difference  between  the  motion  of  a  body  in 
an  ellipse  and  in  a  circle  whose  diameter  AP  is  the  major  axis  of  the 
ellipse. 

NOTE  49,  p.  9.— Apsides.  The  points  P  and  A,  fig.  10,  at  the  ex- 
tremities of  the  major  axis  of  an  orbit.  P  is  commonly  called  the 
perihelion,  a  Greek  term,  signifying  round  the  sun ;  and  the  point  A  is 
called  the  aphelion,  a  Greek  term,  signifying  at  a  distance  from  the  sun. 

NOTE  50,  p.  Q.— Ninety  degrees.  A  circle  is  divided  into  360  equal 
parts,  or  degrees ;  each  degree  into  60  equal  parts,  called  minutes;  and 
each  minute  into  60  equal  parts,  called  seconds.  It  is  usual  to  write 
these  quantities  thus,  15°  16'  10",  which  means  fifteen  degrees,  sixteen 
minutes,  and  ten  seconds.  It  is  clear  that  an  arc  m  n,  fig.  4,  measures 
the  angle  mCn;  hence  we  may  say,  an  arc  of  so  many  degrees,  or  an 
angle  of  so  many  degrees :  for  if  there  be  ten  degrees  in  the  angle 
mCn,  there  will  be  ten  degrees  in  the  arc  mn.  It  is  evident  that  there 
are  90°  in  a  right  angle,  mC  d,  or  quadrant,  since  it  is  the  fourth  part 
of  3600. 

NOTE  51,  p.  9. — Quadratures.  A  celestial  body  is  said  to  be  in  quad- 
rature when  it  is  90  degrees  distant  from  the  sun.  For  example,  in  fig. 
14,  if  d  be  the  sun,  S  the  earth,  and  P  the  moon,  then  the  moon  is  said  to 
be  in  quadrature  when  she  is  in  either  of  the  points  Q,  or  D,  because  the 
angles  dSdand  DSd,  which  measure  her  apparent  distance  from  the 
sun,  are  right  angles. 

NOTE  52,  p.  9.— Eccentricity.  Deviation  from  circular  form.  In  fig. 
6,  C  S  is  the  eccentricity  of  the  orbit,  P  Q  A  D.  Thf  less  C  8,  the  m<»re 


NOTES.  399 

nearly  does  the  orbit  or  ellipse  approach  the  circular  form ;  and  when 
CS  is  zero,  the  ellipse  becomes  a  circle. 

NOTE  53,  p.  9. — Inclination  of  an  torbit.  Let  S,  fig.  12,  be  the  center 
of  the  sun.  P  N  A  it,  the  orbit  jv_.  jg 

of  a  planet  moving  from  west 
to  east  in  the  direction  N  p. 
Let  E  N  m  e  n  be  the  shadow 
or  projection  of  the  orbit  on 
"the  plane  of  the  ecliptic,  then  3? 
N  S  w  is  the  intersection  of 
these  two  planes,  for  theorbif 
rises  above  the  plane  of  the 
ecliptic  toward  Np,  and  sinks 
below  it  at  N  P.  The  angle 
p  N  m,  which  these  two  planes 
make  with  one  another,  is  the  N 

inclination  of  the  orbit  P  N  p  A  to  the  plane  of  the  ecliptic. 

NOTE  54,  p.  9.— Latitude  of  a  planet.  The  angle  p  S  m.  fig.  12,  or  the 
height  of  the  planet  p  above  the  ecliptic  E  N  m.  In  this  case  the  latitude 
is  north.  Thus,  celestial  latitude  is  the  angular  distance  of  a  celestial 
body  frour  the  plane  of  the  ecliptic,  whereas  terrestrial  latitude  is  the 
angular  distance  of  a  place  on  the  surface  of  the  earth  from  the  equator. 

NOTE  55,  p.  lO.—J\Todes.  The  two  points  N  and  a,  fig.  12,  in  which 
the  orbit  N  A  n  P  of  a  planet  or  comet  intersects  the  plane  of  the 
ecliptic  eNEw.  The  part  N  An  of  the  orbit  lies  above  the  plane  of 
the  ecliptic,  and  the  part  nPN  below  it.  The  ascending  node  N  is  the 
point  through  which  the  body  passes  in  rising  above  the  plane  of.  the 
ecliptic,  and  the  descending  node  n  is  the  point  in  which  the  body  sinks 
below  it.  The  nodes  of  a  satellite's  orbit  are  the  points  in  which  it 
intersects  the  plane  of  the  orbit  of  the  planet. 

NOTE  56,  p.  10. — Distance  from  the  sun.  S  p  in  fig.  12.  If  T  be  the 
vernal  equinox,  then  T  Sp  is  the  longitude  of  the  planet  p,  mSp  is  its 
latitude,  and  Sp  its  distance  from  the  sun.  When  these  three  quantities 
are  known,  the  place  of  the  planet  p  is  determined  in  space. 

NOTE  57,  pp.  10,  58. — Elements  of  an  orbit.  Of  these  there  are  seven. 
Let  P  N  A  n,  fig.  12,  be  the  elliptical  orbit  of  a  planet,  C  its  center,  S  the 
sun  in  one  of  the  foci,  T  the  point  of  Aries,  and  E  N  e  n  the  plane  of  the 
ecliptic.  The  elements  are,  the  major  axis  A  P  ;  the  eccentricity  C  S  ; 
the  periodic  time,  that  is,  the  time  of  a  complete  revolution  of  the  body 
in  its  orbit;  and  the  fourth  is  the  longitude  of  the  body  at  any  given  in- 
stant: for  example,  that  at  which  it  passes  through  the  perihelion.  P,  the 
point  of  its  orbit  nearest  to  the  sun.  That  instant  is  assumed  as  the  origin 
of  time,  whence  all  preceding  and  succeeding  periods  are  estimated. 
These  four  quantities  are  sufficient  to  determine  the  form  of  the  orbit  and 
the  motion  of  the  body  in  it.  Three  other  elements  are  requisite  for 
determining  the  position  of  the  orbit  in  space.  These  are,  the  angle 
T  S  P,  the  longitude  of  the  perihelion :  the  angle  A  N  e,  which  is  the 
inclination  of  the  orbit  to  the  plane  of  the  ecliptic  ;  and  lastly,  the  angle 
T  S  N,  the  longitude  of  N  the  ascending  node. 

NOTE  58,  p.  10.—  Whose  planes,  <$-c.  The  planes  of  the  orbits,  as 
P  N  A  n,  fig.  12,  in  which  the  planets  move,  are  inclined  or  make  small 
angles  e  N  A  with  the  plane  of  the  ecliptic  E  N  e  n,  and  cut  it  in  straight 
lines,  N  S  n  passing  through  S  the  center  of  the  sun. 

NOTE  59,  p.  12. — Momentum.  Force  measured  by  the  weight  of  a 
body  and  its  speed,  or  simple  velocity,  conjointly.  The  primitive  momen- 
tum of  the  planets  is,  therefore,  the  quantity  of  motion  which  was  im- 
pressed upon  them  when  they  were  first  thrown  into  space. 

NOTK  60,  p.  12. —  UnftfMf  pfjiiV&rivm.     A  body  is  paid  to  be  in  pqnili- 


400 


NOTES. 


Let  S,  fig.  13,  be  the  sun, 
Fig.  13. 


brium  when  it  is  so  balanced  as  to  remain  at  rest.  But  there  are  two 
kinds  of  equilibrium,  stable  and  unstable.  If  a  body  balanced  in  stable 
equilibrium  be  slightly  disturbed,  it  will  endeavor  to  return  to  rest  by  a 
number  of  movements  to  and  fro,  which  will  continually  decrease  till 
they  cease  altogether,  and  then  the  body  will  be  restored  to  its  original 
state  of  repose.  But  if  the  equilibrium  be  unstable,  these  movements  to 
and  fro,  or  oscillations,  will  become  greater  and  greater  till  the  equili- 
brium is  destroyed. 

NOTE  61,  p.  13. — Retrograde.  Going  backward,  as  from  east  to  west, 
contrary  to  the  motion  of  the  planets. 

NOTE  62,  p.  14. — Parallel  directions.  Such  as  never  meet,  though 
prolonged  ever  so  far: 

NOTE  63,  pp.  14,  16.—  The  whole  force,  be. 
Nmw  the  plane  of  the  ecliptic,^  the  dis- 
turbed planet  moving  in  its  orbit  7ipN,  and 
d  the  disturbing  planet.  Now,  d  attracts  the 
sun  and  the  planet^  with  different  intensities 
in  the  directions  d  S,  dp  :  the  difference  only 
of  these  forces  disturbs  the  motion  of  p  ;  it 
is,  therefore,  called  the  disturbing  force.  But 
this  whole  disturbing  force  may  be  regarded 
as  equivalent  to  three  forces,  acting  in  the 
directions  p  S,  p  T,  and  p  m.  The  force  act- 
ing in  the  radius  vector  p  S,  joining  the  cen- 
ters of  the  sun  and  planet,  is  called  the 
radial  force.  It  sometimes  draws  the  dis- 
turbed planet  p  from  the  sun,  and  sometimes 
brings  it  nearer  to  him.  The  force  which 
acts  in  the  direction  of  the  tangent,  p  T, 
is  called  the  tangential  force.  It  disturbs 
the  motion  of  p  in  longitude,  that  is,  it  accel- 
erates its  motion  in  some  parts  of  its  orbit 
and  retards  it 
in  others,  so 
that  the  ra- 
dius vector 
S  p  does  not 
move  over 
equal  areas 

in  equal  times.  (See  Note  26.)  Forexam- 
~  pie,  in  the  position  of  the  bodies  in  fig.  14, 
it  is  evident  that,  in  consequence  of  the 
attraction  of  d,  the  planet  P  will  have  its 
motion  accelerated  from  Q,  to  C,  retarded 
from  C  to  D,  again  accelerated  from  D  to 
O,  and,  lastly,  retarded  from  O  to  Q,.  The 
disturbing  body  is  here  supposed  to  be  at 
rest,  and  the  orbit  circular ;  but  as  both 
bodies  are  perpetually  moving  with  dif- 
ferent velocities  in  ellipses,  the  perturba- 
tions or  changes  in  the  motions  of  P  are 
very  numerous.  Lastly,  that  part  of  the 
disturbing  force  which  acts  in  the  direc- 
tion of  a  line  p  m,  fig.  13,  at  right  angles 
to  the  plane  of  the  orbit  N pn,  may  be 
called  the  perpendicular  force.  It  some- 
times causes  the  body  to  approach  nearer, 
nnd  aornptimp--  to  rfredp  fnrthf>r  from,  the 


NOTES. 


401 


plane  of  the  ecliptic,  N  m  n,  than  it  would  otherwise  do.  The  action  of 
the  disturbing  forces  is  admirably  explained  in  a  work  on  gravitation  by 
Professor  Airy,  of  Cambridge. 

NOTE  64,  pp.  16,  69.— Perihelion.  Fig.  10,  P,  the  point  of  an  orbit 
nearest  the  sun. 

NOTE  65,  p.  16.— Aphelion.  Fig.  10,  A,  the  point  of  an  orbit  farthest 
from  the  sun. 

NOTE  66,  pp.  16,  ib.,  17.  In  fig.  15  the  central  force  is  greater  than  the 
exact  law  of  gravity  ;  therefore  the  curvature  Ppa  is  greater  than  Pp  A 
the  real  ellipse  ;  hence  the  planet  p  comes  lo  the  point  a,  called  the  aphe- 
lion, sooner  than  if  It  moved  in  the  orbit  Pp  A,  which  makes  the  line 
PSA  advance  to  a.  In  fig.  16,  on  the  contrary,  the  curvature  P  p  a  is 
Fig.  15.  Fig.  16. 


less  than  in  the  true  ellipse,  so  that  the  planet  p  must  move  through 
more  than  the  arc  Pp  A,  or  180°,  before  it  comes  to  the  aphelion  a,  which 
causes  the  greater  axis  P  S  A  to  recede  to  a. 

NOTE  67,  pp.  16,  17. — Motion  of  apsides. 
Let  PSA,  fig.  17,  be  the  position  of  the 
elliptical  orbit  of  a  planet  at  any  time  ; 
then,  by  the  action  of  the  disturbing 
forces,  it  successively  takes  the  position 
P'  S  A',  P"  S  A",  &c.,  till  by  this  direct 
motion  it  has  accomplished  a  revolution, 
and  then  it  begins  again  ;  so  that  the 
motion  is  perpetual. 


NOTE  68,  p.  J6.— Sidereal  revolution. 
The  consecutive  return  of  an  object  to 
the  same  star. 


NOTE  69,  p.  16. —  Tropical  revolution. 
object  to  the  same  tropic  or  equinox. 

NOTE  70,  p.  17.—  The  orbit  only  bulges, 
&-c.  In  fig-  18  the  effect  or  the  varia- 
tion in  the  eccentricity  is  shown,  where 
Pp  A  is  the  elliptical  Orbit  at  any  given 
instant:  after  a  time  it  will  take  the 
form  P  p'  A,  in  consequence  of  the 
decrease  in  the  eccentricity  CS ;  then 
the  form?  Pp"  A.Pp'"  A,"&c.,  conse- 
cutively  from  the  same  cause,  and  as  *• 
the  mHjor  axis  P  A  always  retains  the 
name  length,  the  orbit  approaches  more 
»nd  more-  nearly  to  the  circular  form. 
But  after  this  has  pone  on  for  some 
thousands  of  years,  the  orbit  contracts 
aeain,  and  become*  more  and  more 
elliptical. 

26  L  L2 


--..U-" 

K 

The  consecutive  return  of  an 

Fig.  18. 


402 


NOTES. 


NOTE  71,  pp.  18,  19.—  The  ecliptic  is  the  apparent  path  of  the  sun  in 
the  heavens.  See  Note  46. 

NOTE  72,  p.  18.—  This  force  tends  to  pull,  <$-c.  The  force  in  question 
acting  in  the  direction  pm,  fig.  13,  pulls  the  planet  p  toward  the  plane 
N  m  M,  or  pushes  it  farther  above  it,  giving  the  planet  a  tendency  to  move 
in  an  orbit  above  or  below  its  undisturbed  orbit  N^n,  which  alters  the 
angle  p  N  m,  and  makes  the  node  N  and  tbe  line  of  nodes  N  n  change 
their  positions. 

NOTE  73,  p.  18.— Motion  of  the  nodes.  Let  S,  fig.  19,  be  the  sun  ;  S  N  n 
the  plane  of  the  ecliptic;  P  the  disturbing  body;  and  p  a  planet  moving 
in  its  orbit  p  n,  of  which  p  n  is  so  small  a  part  that  it  is  represented  as  a 
straight  line.  The  plane  Snp  of  this  orbit  cuts  the  plane  of  the  ecliptic 
in  the  straight  line  S  M.  Suppose  the  disturbing  force  begins  to  act  on  p 
so  as  to  draw  the  planet  into  the  arc  pp' ;  then,  instead  of  moving  in 
the  orbit  p  n,  it  will  tend  to  move  in  the  orbit  pp'n',  whose  plane  cuts 
the  ecliptic  in  the  straight  line  S  n.  If  the  disturbing  force  acts  again 
upon  the  body  when  at  p',  so  as  to  draw  it  into  the  arcy  p",  the  planet 
will  now  tend  to  move  in  the  orbit  p' p"  n",  whose  plane  cuts  the  ecliptic 
in  the  straight  line  S  n".  The  action  of  the  disturbing  force  on  the 
planet  when  at  p'',  will  bring  the  node  to  n'",  and  so  on.  In  this  man- 
ner the  node  goes  backward  through  the  successive  points,  n,n',n",n"\ 
&c.,  and  the  line  of  nodes  S  n  has  a  perpetual  retrograde  motion  about 


S,  the  center  of  the  sun.  The  disturbing  force  has  been  represented  as 
acting  at  intervals  for  the  sake,  of  illustration  :  in  nature  it  is  continuous, 
so  that  the  motion  of  the  node  is  continuous  also  ;  though  it  is  sometimes 
rapid  and  sometimes  slow,  now  retrograde  and  now  direct;  but  on  the 
whole,  the  motion  is  slowly  retrograde. 

NOTE  74,  p.  18. —  When  the  disturbing  planet  is  anywhere  in  the  line 
SN,  fig.  19,  or  in  its  prolongation,  it  is  in  the  same  plane  with  the  dis- 
turbed planet;  and  however  much  it  may  affect  its  motions  in  that 
plane,  it  can  have  no  tendency  to  draw  it  out  of  it.  But  when  the 
disturbing  planet  is  in  P,  at  right  angles  to  the  line  S  N,  and  not  in  the 
plane  of  the  orbit,  it  has  a  powerful  effect  on  the  motion  of  the  nodes  : 
between  these  two  positions  there  is  great  variety  of  action. 

NOTE  75,  p.  19. —  The  changes  in  the  inclination  are  extremely  minute 
when  compared  with  the  motion  of  the  node,  ns  evidently  appears  front 
fig.  19,  where  the  angles  npn',  n' p'  n",  &c.  are  much  smaller  than  the 
corresponding  angles  n  S  n',  S  n",  &c. 

NOTE  76,  p.  20.—  Sines  and  cosines.  Figure  4  is  a  circle ;  n.p  K  the 
sine,  and  Cp  is  the  cosine  of  an  arc  mn.  Suppose  the  radius  Cm  to 
begin  to  revolve  at  m,  in  the  direction  mna;  then  at  the  point  m  the 
sign  is  zero,  and  the  cosine  is  equal  to  the  radius  Cm.  As  the  line  C  m 


i\OTES. 


403 


revolves  and  takes  the  successive  positions  Cn,  Co,  C'6,  &.C.,  the  sines* 
n p,  aq,  br,  &LC.  of  the  arcs  7/171,  ma,  mh,  &c.  increase,  while  the  corres 
ponding  cosines  ( '  /<.  C  q,  C  r,  &c.  decrease,  and  when  the  revolving  radius 
takes  the  position  (.'</,  ut  right  angles  to  the  diameter  g  »i,  the  sine  be- 
comes equal  to  the  radius  Cd,  and  the  cosine  is  zero.  After  passing  the 
point  (/.  the  contrary  happens;  for  the  sines eK,  IV,  &c.  diminish,  and 
the  cosines  CK,  C  V,  &.c.  go  on  increasing,  till  at  g  the  sine  is  zero,  and 
the  cosine  is  equal  to  the  radius  C  g.  The  same  alternation  takes  place 
through  the  remaining  parts  g  A,  A?/»,  of  the  circle,  so  that  a  sine  or  cosine 
never  can  exceed  the  radius.  As  the  rotation  of  the  earth  is  invariable, 
each  point  of  its  surface  passes  through  a  complete  circle,  or  360  degrees, 
in  twenty-four  hours,  at  a  rate  of  15  degrees  in  an  hour.  Time,  there- 
fore, becomes  a  measure  of  angular  motion,  and  vice  versd,  the  arcs  of  a 
circle  a  measure  of  time,  since  these  two  quantities  vary  simultaneously 
and  equably,  and  as  the  sines  and  cosines  of  the  arcs  are  expressed  in 
terms  of  the  time,  they  vary  with  it.  Therefore,  however  long  the  time 
may  be,  and  how  often  soever  the  radius  may  revolve  round  the  circle, 
the  sines  and  cosines  never  can  exceed  the  radius ;  and  us  the  radius  is  as- 
sumed to  be  equal  to  unity,  their  values  oscillate  between  unity  and  zero. 

NOTE  77,  p.  21. — The  small  eccentricities  and  inclinations  of  the  plan- 
etary orbits,  and  the  revolutions  of  all  the  bodies  in  the  sarae  direction, 
were  proved  by  Euler,  La  Grange,  and  La  Place,  to  be  conditions  neces- 
sary for  the  stability  of  the  solar  system.  Recently,  however,  the  peri- 
odicity of  the  terms  of  the  series  expressing  the  perturbations  was  sup- 
posed to  be  sufficient  alone,  but  M.  Poisson  has  shown  that  to  be  a  mistake  ; 
that  these  three  conditions  are  requisite  for  the  necessary  convergence 
of  the  series,  and  that  therefore  the  stability  of  the  system  depends  on 
them  conjointly  with  the  periodicity  of  the  sines  and  cosines  of  each 
term.  The  author  is  aware  that  this  note  can  only  be  intelligible  to  the 
analyst,  but  she  is  desirous  of  correcting  an  error,  and  the  more  so  as  the 
conditions  of  stability  afford  one  of  the  most  striking  instances  of  design 
in  the  original  construction  of  our  system,  and  of  the  foresight  and  su- 
preme wisdom  of  the  Divine  Architect. 

NOTE  78,  p.  21. — Resisting  medium.  A  fluid  which  resists  the  motions 
of  bodies  such  as  atmospheric  air,  or  the  highly  elastic  fluid  called  ether, 
with  which  it  is  presumed  that  space  is  filled. 

NOTK  79,  p.  22.—  Obliquity  of  the  ecliptic.  The  angle  e  T  q,  fig.  11,  be- 
tween the  plane  of  the  terrestrial  equator  q  T  Q,  and  the  plane  of  the  eclip 
tic  E  T  e.  The  obliquity  is  variable. 

A'OTK  80,  p.  2-2.— Invariable  p'ane.    In  the  earth  the  equator  is  the  ia- 


Fig.  20 


404 


NOTES. 


variable  plane  which  nearly  maintains  a  parallel  position  with  regard  to 
itself  while  revolving  about  the 'sun,  as  in  fig.  20,  where  EQ  represents 
it.  The  two  hemispheres  balance  one  another  on  each  side  of  this  plane, 
and  would  still  do  so  if  al!  the  particles  of  which  they  consist  were  mov- 
able among  themselves,  provided  the  earth  were  not  disturbed  by  the 
action  of  the  sun  and  moon,  which  alters  the  parallelism  of  the  equator 
by  the  small  variation  called  nutation,  to  be  explained  hereafter. 

NOTE  81,  p.  23.     If  each  particle,  <J-c.     Let  P,  P',  P",  foe.,  fig.  21,  be 
planets  moving  in  their  orbits  about  the  center  of  gravity  of  the  system. 

Fig.  21. 


Let  P  S  M,  P'  S  M',  &c.  be  portions  of  these  orbits  moved  over  by  the  radii 
vectores,  S  P,  S  P',  foe.,  in  a  given  time,  and  let  p  S  m,  p'  S  m'  &c.  be  their 
shadows  or  projections  on  the  invariable  plane.  Then,  if  the  numbers 
which  represent  the  masses  of  the  planets,  P,  P'  &c.  be  respectively  mul- 
tiplied by  the  numbers  representing  the  areas  or  spaces  p  S  m,  p'  S »«',  &c. 
the  sum  of  the  whole  will  be  greater  for  the  invariable  plane  than  it 
would  be  for  any  plane  that  could  pass  through  S,  the  center  of  gravity 
of  the  system. 

NOTE  82,  p.  23.—  The  center  of  gravity  of  the  solar  system  lies  within 
the  body  of  the  sun,  because  his  mass  is  much  greater  than  the  masses 
of  all  the  planets  and  satellites  added  together. 

NOTE  83,  pp.  24,  35. — Conjunction.  A  planet  is  said  to  be  in  conjunc- 
tion when  it  has  the  same  longitude  with  the  sun,  and  in  opposition 
when  its  longitude  differs  from  that  of  the  sun  by  180  degrees.  Thus  two 
bodies  are  said  to  be  in  conjunction  when  they  are  seen  exactly  in  the 
same  part  of  the  heavens,  nnd  in  opposition  when  diametrically  opposite 
to  one  another'.  Mercury  and  Venus,  which  are  nearer  to  the  sun  than 
the  earth,  are  called  inferior  planets,  while  all  the  others,  being  farther 
from  the  sun  than  the  earth,  are  said  to  be  superior  planets.  Suppose 
the  earth  to  be  atE,  figure  24  ;  then  a  superior  planet  will  be  in  conjunc- 
tion with  the  sun  at  C,  and  in  opposition  to  him  when  at  O.  Again, 
suppose  the  earth  to  be  in  O,  then  an  inferior  planet  will  be  in  conjunc- 
tion when  at  E,  and  in  opposition  when  at  F. 

NOTE  84,  p.  25. —  The  periodic  inequalities  are  computed  for  a  given 
time ;  and  consequently  for  a  given  form  and  position  of  the  orbits  of  the 
disturbed  and  disturbing  bodies.  Although  the  elements  of  the  orbits 
vary  so  slowly  that  no  sensible  effect  is  produced  on  inequalities  of  a 
short  period  ;  yet,  in  the  course  of  time,  the  secular  variations  of  the  ele- 
ments change  the  forms  and  relative  positions  of  the  orbits  so  much,  that 
Jupiter  and  Saturn,  which  would  have  come  to  the  same  relative  positions 
with  regard  to  the  sun  and  to  one  another  after  850  years,  do  not  arrive 
at  the  same  relative  positions  till  after  918  years. 


NOTES.  405 

NOTE  85,  p.  25.— Conf/rvration.  The  relative  position  of  the  planets 
with  regard  to  one  another,  to  the  sun,  and  to  the  plane  of  the  ecliptic. 

NOTE  86,  p.  26. — In  the  same  manner  that  the  eccentricity  of  an  ellipti- 
cal orLit  may  be  increased  or  diminished  by  the  action  of  the  disturbing 
forces,  so  a  circular  orbit  may  acquire  less  or  more  ellipticity  from  the 
same  cause:  It  is  thus  that  the  forms  of  the  orbit  of  the  first  and  second 
satellites  of  Jupiter  oscillate  between  circles  and  ellipses  differing  very 
little  from  Circles. 

NOTE  87,  p.  27. —  The  plane  of  Jupiter's  equator  is  the  imaginary  plane 
passing  through  his  center  at  right  angles  to  his  axis  of  rotation  ;  and 
corresponds  to  the  plane  qEQe,  in  fig.  1.  The  satellites  move  very 
nearly  in  the  plane  of  Jupiter's  equator,  for  if  J  be  Jupiter,  fig.  22,  Pp  his 


axis  of  rotation,  eQ,  his  equatorial  diameter,  which  is  6000  miles  longer 
than  Pp,  and  if  JO  and  J  E  be  the  planes  of  his  orbit  and  equator  seen 
edgewise,  then  the  orbits  of  his  four  satellites  seen  edgewise  will  have 
the  positions  J  1,  J  2,  J  3,  J  4.  These  are  extremely  near  to  one  another, 
for  the  angle  E  J  O  is  only  3°  5'  30". 

NOTE  88,  p.  27. — In  consequence  of  the  satellites  moving  so  nearly  in 
the  plane  of  Jupiter's  equator,  when  seen  from  the  earth,  they  appear  to 
be  always  very  nearly  in  a  straight  line,  however  much  they  may  change 
their  positions  with  regard  to  one  another  and  to  their  primary.  For 
example,  on  the  evenings  of  the  3d,  4th,  5th,  and  6th  of  January,  1835, 
the  satellites  had  the  configurations  given  in  fig.  23,  where  O  is  Jupiter, 

Fig.  23. 
J!»»-  W«i  Ea« 


3 

2. 

/.    O     3- 

•'h 

A  ! 

3. 

•2    O          •/ 

•A 

5    j 

•3                /. 

O                   -2 

A. 

6  1 

•  3 

£)        /• 

A.' 

and  1, 2.  3,  4,  are  the  first,  second,  third,  and  fourth  satellites.  The  satel- 
lite is  supposed  to  be  moving  in  a  direction  from  the  figure  toward  the 
point.  On  the  sixth  evening  th«  second  satellite  was  seen  on  the  disc  of 
the  planet. 

NOTE  89,  p.  28.— Angular  motion  or  velocity  is  the  swiftness  with 
which  a  body  revolves — a  sling,  for  example  ;  or  the  speed  with  which 
the  surface  of  the  earth  performs  its  daily  rotation  about  its  axis. 

NOTE  90,  p.  ^.—Displacement  of  Jupiter's  orbit.  The  action  of  the 
planets  occasions  secular  variations  in  the  position  of  Jupiter's  orbit,  J  O, 
fig.  22,  without  affecting  the  plane  of  his  equator,  J  E.  Again,  the  sun 
and  satellites  themselves,  by  attracting  the  protul>erant  matter  at  Jupiter's 
equator,  change  the  position  of  the  plane  J  E  without  affecting  J  O.  Both 
of  these  cause  j»erturbations  in  the  motions  of  the  satellites. 

NOTE  91,  p.  26.— Precession,  with  regard  to  Jupiter,  is  a  retrograde 
notion  of  the  point  where  the  lines  JO,  J  E,  intersect  fig.  22, 


406 


NOTES. 


NOTE  92,  p.  29.— Synodic  motion  of  a  satellite.  Its  motion  during  the 
interval  between  two  of  its  consecutive  eclipses. 

NOTE  93,  p.  29.— Opposition.  A  body  is  said  \n  be  in  opposition  when 
its  longitude  differs  from  that  of  the  sun  by  18(P.  If  S,  fig.  24,  be  the 


Fig.  24. 


sun,  and  E  the  earth,  then  Jupiter  is  in  opposition  when  at  O,  and  in 
conjunction  when  at  C.  In  these  positions  the  three  bodies  are  in  the 
same  straight  line. 

NOTE  94,  p.  29.— Eclipses  of  the 
satellites.  Let  S,  fig.  25,  be  the  sun, 
J  Jupiter,  and  a  B  b  his  shadow.  Let 
the  earth  be  moving  in  its  orbit, 
in  the  direction  EARTH,  and  the 
third  satellite  in  the  direction  abmn. 
When  the  earth  is  at  E,  the  satellite, 
in  moving  through  the  arc  a  b,  will 
vanish  at  a,  and  reappear  at  b,  on  the 
same  side  of  Jupiter.  If  the  earth  be 
in  R,  Jupiter  will  be  in  opposition; 
and  then  the  satellite,  in  moving 
through  the  arc  a  b,  will  vanish  close 
to  the  disc  of  the  planet,  and  will  re- 
appear on  the  other  side  of  it.  But  if 
the  satellite  be  moving  through  the 
arc  m  n,  it  will  appear  to  pass  over 
the  disc  and  eclipse  the  planet. 

NOTE  95,  pp.  30,  42. — Meridian.    A 
terrestrial  meridian  is  a  line  passing 
round  the   earth   and   through    both 
poles.    In  every  part  of  it  noon  hap- 
pens at  the  same  instant.    In  figures 
1  and  3,  the  lines  N  Q  S  and  N  G  S 
are  meridians,  C  being  the  center  of 
the  earth,  and  N  S  its  axis  of  rotation. 
The   meridian    passing   through  the 
Observatory  at  Greenwich  is  assumed        , 
by  the  British  as  a  fixed  origin  from        / 
whence  terrestrial  longitudes  are  mea-    i1,' 
eured.    And  as  each  point  on  the  sur- 
face of  the  earth  passes  through  300°, 
or  a  complete  circle  in  twenty-four 


NOTES.  407 

Aours,  at  the  rate  of  15  degrees  in  an  hour,  time  becomes  a  representative 
of  angular  motion.  Hence  if  the  eclipse  of  a  satellite  happens  at  any 
place  at  eight  o'clock  in  the  evening,  and  the  Nautical  Almanac  shows 
that  the  same  phenomenon  will  take  place  at  Greenwich  at  nine,  the 
place  of  observation  will  be  in  the  15°  of  west  longitude. 

NOTE  96,  p.  30.— Conjunction.  Let  S  be  the  sun,  fig.  24,  E  the  earth, 
and  J  OJ'  C'  the  orbit  of  Jupiter.  Then  the  eclipses  which  happen  when 
Jupiter  is  in  O  are  seen  16m  26»  sooner  than  those  which  take  place  when 
the  planet  is  inC.  Jupiter  is  in  conjunction  when  at  C  and  in  opposition 
when  in  O. 

NOTE  97,  p.  30.— In  the  diagonal,  Src.  Were  the  line  A  S,  fig.  26, 
100,000  times  longerthan^  A  B,  Jupiter's  true  place  Fig.  26. 

would  be  in  the  direction  A  S',  the  diagonal  of  the  „,   „ 

figure  A  B  S' S,  which  is,  of  course,  out  of  propor- 
tion. 

NOTE  98,  p.  31.— Aberration  of  light.  The  ce- 
lestial bodies  are  so  distant,  that  the  rays  of  light 
coming  from  them  may  be  reckoned  parallel. 
Therefore,  let  S  A,  S'  B,  fig.  26,  be  two  rays  of  light 
coming  from  the  sun,  or  a  planet,  to  the  earth 
moving  in  its  orbit  in  the  direction  A  B.  If  a  tele- 
scope be  held  in  the  direction  A  S,  the  ray  S  A, 
instead  of  going  down  the  tube,  will  impinge  on  its 
side,  and  be  lost  in  consequence  of  the  telescope 
being  carried  with  the  earth  in  the  direction  A  B. 
But  if  the  tube  be  held  in  the  position  A  E,  so  that 
A  B  is  to  A  S  as  the  velocity  of  the  earth  to  the 

velocity  of  light,  the  ray  will  pass  through  S'  E  A. 

The  star  appears  to  be  in  the  direction  A  S,  when 

it  really  is  in  the  direction  A  S',  hence  the  angle  S  A  S'  is  the  angle  of 

aberration.. 

NOTE  99,  p.  31. — Density  proportional  to  elasticity.  The  more  a  fluid, 
such  as  atmospheric  air,  is  reduced  in  dimensions  by  pressure,  the  more 
it  resists  the  pressure. 

NOTE  100,  p.  32. —  Oseillation»  of  pendulum  retarded.  If  a  clock  be 
carried  from  the  pole  to  the  equator,  its  rate  will  be  gradually  diminished, 
that  is,  it  will  go  slower  and  slower,  because  the  centrifugal  force  which 
increases  from  the  pole  to  the-equator,  diminishes  the  force  of  gravity. 

NOTE  101,  p.  33. — Disturbing  action.  The  disturbing  force  acts  here 
in  the  very  same  manner  as  in  note  63 ;  only  that  the  disturbing  body  d, 
fig.  14,  is  the  sun,  S  the  earth,  and  p  the  moon. 

NOTE  102.  pp.  34,  36,  81. — Perigee.  A  Greek  word  signifying  round 
the  earth.  The  perigee  of  the  lunar  orbit  is  the  point  P,  fig.  6,  where  the 
moon  i»  nearest  to  the  earth.  It  corresponds  to  the  perihelion  of  a  planet. 
Sometimes  the  word  is  used  to  denote  the  point  where  the  sun  is  nearest 
to  the  earth. 

NOTE  103,  p.  34.— Eveetion.  The  evection  is  produced  by  the  action  of 
the  radial  force  in  the  direction  S  p,  fig.  14,  which  sometimes  increases 
and  sometimes  diminishes  the  earth's  attraction  to  the  moon.  It  produces 
a  corresponding  temporary  change  in  the  eccentricity,  which  varies  with 
the  position  of  the  major  axis  of  the  lunar  orbit  in  respect  of  the  line  S  d, 
joining  the  centers  of  the  earth  and  sun. 

NOTE  104,  p.  34. — Variation.  The  lunar  perturbation  called  the  varia- 
tion is  the  alternate  acceleration  and  retardation  of  the  moon  in  longitude, 
from  the  action  of  the  tangentlnl  force.  She  is  accelerated  in  going  from 
quadratures  in  Q  and  D,  fig.  14,  to  the  points  C  and  O,  called  syzygies, 
BJid  i»  retarded  in  going  from  the  syzygies  C  and  O  to  Q  and  D  again. 


408 


NOTES. 


NOTE  105,  p.  36. — Square  of  time.  If  the  times  increase  at  tlie  rate  of 
1,  2,  3,  4,  &c.,  years  or  hundreds  of  years,  the  squares  of  the  times  will 
be  1,  4,  9,  16,  &c.,  years  or  hundreds  of  years. 

NOTE  106,  p.  37. — Mean  anomaly.  The  mean  anomaly  of  a  planet  is 
its  angular  distance  from  the  perihelion,  supposing  it  to  move  in  a  circle. 
The  true  anomaly  is  its  angular  distance  from  the  perihelion  in  its  ellip- 
tical orbit.  For  example,  in  fig.  10,  the  mean  anomaly  is  PC  m,  and  the 
true  anomaly  is  P  S  p. 

NOTE  107,  pp.  38,  63.— Many  circumferences.  There  are  360  degrees, 
or  1,296,000  seconds,  in  a  circumference  ;  and  as  the  acceleration  of  the 
moon  only  increases  at  the  rate  of  eleven  seconds  in  a  century,  if.  must 
be  a  prodigious  number  of  ages  before  it  accumulates  to  many  circum- 
ferences. 

NOTE  108,  p.  38.— Phases  of  the  moon.  The  periodical  changes  in  the 
enlightened  part  of  her  disc  from  a  crescent  to  a  circle,  depending  upon 
her  position  with  regard  to  the  sun  and  earlh. 

NOTE  109,  p.  39. — Lunar  eclipse.  Let  S,  fig.  27,  be  the  sun,  E  the 
earth,  and  m  the  moon.  The  space  a  A  b  is  a  section  of. the  shadow, 

Fig.  27. 


-   d 


which  has  the  form  of  a  cone  or  sugar-loaf,  and  the  spaces  A  a  c,  A  b  d, 
are  the  penumbra.  The  axis  of  the  cone  passes  through  A,  and  through 
E  and  S,  the  centers  of  the  sun  and  earth,  and  n  m  n'  is  the  path  of  the 
moon  through  the  shadow. 

NOTE  110r  p.  39.— Apparent  diameter.  The  diameter  of  a  celestial  body 
as  seen  from  the  earth. 

NOTE  111,  p.  39. — Penumbra.  The  shadow,  or  imperfect  darkness, 
which  precedes  and  follows  an  eclipse. 

NOTE  112,  p.  39.-  -Synodic  revolution  of  the  moon.  The  time  between 
two  consecutive  now  or  full  moons. 

NOTE  113,  p.  39.  Horizontal  refraction.  The  light,  in  coming  from  a 
celesiial  object,  is  ben.  into  a  curve  as  soon  as  it  enters  our  atmosphere, 
and  that  bending  is  greatest  when  the  object  is  in  the  horizon. 

NOTE  114,  p.  40.— Solar  eclipse.  Let  S,  fig.  28,  be  the  sun,  m  the  moon, 
and  E  the  earth.  Then  a  E  b  is  the  moon's  shadow,  which  sometimes 


Fig.  28. 


NOTES. 


409 


eclipses  a  small  portion  of  the  earth's  surface  at  e,  and  sometimes  falls 
short  of  it.  To  a  person  at  e,  in  the  center  of  the  shadow,  the  eclipse 
may  be  total  or  annular;  to  a  person  not  in  the  center  of  the  shadow,  a 
part  of  the  sun  will  be  eclipsed  ;  and  to  one  at  the  edge  of  the  shadow 
there  will  be  no  eclipse  at  all.  The  spaces  P  b  E,  P'  a  E  are  the  pen- 
umbra. 

Fisr.  29. 


NOTE  115,  p.  42. — From  the  extremities,  <J-c. 
If  the  length  of  the  line  a  b,  fig.  29,  be  meas- 
ured, in  feet  or  fathoms,  the  angles  S  b  a, 
Sab,  can  be  measured,  and  then  the  angle 
oS  b  is  known,  whence  the  length  of  the  line 
S  C  may  be  computed,  a  S  b  is  the  parallax 
of  the  object  S,  and  it  is  clear  that  the  greater 
the  distance  of  8,  the  less  the  base  a  b  will 
appear,  because  the  angle  a  S'  b  is  less  than 
a  3  ft. 


NOTE  116,  p.  43.— Every  particle  will  describe  a  circle,  Src.  If  N  S,  fig. 
3,  be  the  axis  about  which  the  body  revolves,  then  particles  at  B,  Q, 
&c.,  will  whirl  in  the  circles  B  G  A  a,  <J  E  qd,  whose  centers  are  in  the 
axis  N  S,  and  their  planes  parallel  to  one  another.  They  are,  in  fact, 
parallels  of  latitude,  Q.  E  q  d  being  the  equator. 

NOTK  117,  p.  43.— The  force  of  gravity,  &c.  Gravity  at  the  equator 
acts  in  the  direction  d  C,  fig.  30 ;  whereas  the  direction  of  the  centrifugal 
Fiff.30. 


MM 


410  NOTES. 

force  is  exactly  contrary,  being  in  the  direction  C  Q, ;  hence,  the  differ- 
ence of  the  two  is  the  force  called  gravitation,  which  makes  bodies  fall 
to  the  surface  of  the  earth.  At  any  point,  m,  not  at  the  equator,  the 
direction  of  gravity  is  m  b,  perpendicular  to  the  surface  ;  but  the  centri- 
fugal force  acts  perpendicularly  to  N  S,  the  axis  of  rotation.  Now  the 
effect  of  the  centrifugal  force  is  the  same  as  if  it  were  two  forces,  one  of 
which,  acting  in  the  direction  b  m,  diminishes  the  force  of  gravity  ;  and 
another  which,  acting  in  the  direction  m  t,  tangent  to  the  surface  at  m, 
urges  the  particles  toward  Q,  and  tends  to  swell  out  the  earth  at  the 
equator. 

NOTE  118,  p.  44. — Homogeneous  mass.  A  quantity  of  matter,  every- 
where of  the  same  density. 

NOTE  119,  p.  44.— Ellipsoid  of  revolution.  A  solid  formed  by  the  revo- 
lution of  an  ellipse  about  its  axis.  If  the  ellipse  revolve  about  its  minor 
axis  Q,  D,  fig.  6,  the  ellipsoid  will  be  oblate,  or  flattened  at  the  poles  like 
an  orange.  If  the  revolution  be  about  the  greater  axis  A  P,  the  ellipsoid 
will  be  prolate,  like  an  egg. 

NOTE  120,  p.  44. — Concentric  elliptical  strata.  Strata,  or  layers,  having 
an  elliptical  form  and  the  same  center. 

NOTE  121,  p.  45.— On  the  whole,  be.  The  line  N  Q  S  q,  fig.  1,  repre- 
sents the  ellipse  in  question,  its  major  axis  being  Q,  q.  its  minor  axis  N  S. 

NOTE  122,  p.  45.— Increase  in  the  length  of  the  radii,  Src.  The  radii 
gradually  increase  from  the  polar  radius  C  N,  fig.  30,  which  is  least,  to 
the  equatorial  radius  C  Q.,  which  is  greatest.  There  is  also  an  increase 
in  the  lengths  of  the  arcs  corresponding  to  the  same  number  of  degrees 
from  the  equator  to  the  poles,  for  the  angle  N  C  r,  being  equal  to  q  Cd, 
the  elliptical  arc  N  r  is  less  than  q  d. 

NOTE  123,  pp.  45,  259.—  Cosine  of  latitude.  The  angles  mCa,mCb,  fig. 
4,  being  the  latitudes  of  the  points  a,  b,  &c.,  the  cosines  are  C  q,  C  r,  &c. 

NOTE  124,  p.  46.— An  arc  of  the  meridian.  Let  N  Q  S  g,  fig.  30,  be  the 
meridian,  and  m  n  the  arc  to  be  measured.  Then  if  Z'  m,  Z  n,  be  verti- 
cals, or  lines  perpendicular  to  the  surface  of  the  earth,  at  the  extremities 
of  the  arc  m  n  they  will  meet  in  p.  Q,an,Q,b  m,  are  the  latitudes  of  the 
points  m  and  n,  and  their  difference  is  the  angle  mpn.  Since  the  lati- 
tudes are  equal  to  the  height  of  the  pole  of  the  equinoctial  above  the 
horizon  of  the  places  m  and  ?t,  the  angle  mpn  may  be  found  by  observa- 
tion. When  the  distance  m  n  is  measured  in  feet  or  fathoms,  and  divided 
by  the  number  of  degrees  and  parts  of  a  degree  contained  in  the  angle 
mpn,  the  length  of  an  arc  of  one  degree  is  obtained. 

NOTE  125,  p.  46.— Ji  scries  of  triangles.    Let  M  M',  fig.  31,  be  the 


Fig.M. 


meridian  of  any  place.  A  line,  A  B,  is  measured  with  rods,  on  level 
ground,  of  any  number  of  fathoms,  C  being  some  point  seen  from  both 
ends  of  it.  As  two  of  the  angles  of  the  triangle  ABC  can  be  measured, 
the  lengths  of  the  sides  A  C,  B  C,  can  be  computed ;  and  if  the  angle 
m  A  B,  which  the  base  A  B  makes  with  the  meridian,  be  measured,  the 
length  of  the  sides  B  m,  A  /«,  may  be  obtained  by  computation,  so  that 


NOTES. 


411 


A  «,  a  small  part  of  the  meridian,  is  determined.  Again,  if  D  be  a  point 
visible  from  the  extremities  of  the  known  line  BC,  two  of  the  angles  of 
the  triangle  BCD  may  be  measured,  and  the  length  of  the  sides  CD, 
BD,  computed.  Then  if  the  angle  Emm'  he  measured,  all  the  angles 
and  the  side  B  m  of  the  triangle  Emm'  are  known,  whence  the  length  of 
the  line  m  m'  may  lie  computed,  so  that  the  portion  A  m'  of  the  meridian 
is  determined,  and  in  the  same  manner  it  may  be  prolonged  indefinitely. 

NOTE  126,  pp.  47. 48.—  The  square  of  the  sine  of  the  latitude.  Q.  b  m,  fig. 
30.  being  the  latitude  ofm,em  is  the  sine,  and  b  e  the  cosine.  Then  the 
number  expressing  the  length  of  em,  multiplied  by  itself,  is  the  square  of 
the  sine  of  the  latitude ;  and  the  number  expressing  the  length  of  A  «, 
multiplied  by  itself,  is  the  square  of  the  cosine  of  the  latitude. 

NOTE  127,  p.  49. — A  pendulum  is  that  part  of  a  clock  which  swings  to 
and  fro. 

NOTK  128,  p.  51.— Parallax.  The  angle  aSft,  fig.  29,  under  which  we 
view  an  object  a  b :  it  therefore  diminishes  as  the  distance  increases.  The 
parallax  of  a  celestial  object  is  the  angle  which  the  radius  of  the  earth 
would  lie  seen  under,  if  viewed  from  that  object.  Let  E,  fig.  32,  be  the 


Fig.  32. 


center  of  the  earth.  E  H  .ts  radius,  and  m  H  O  the  horizon  of  an  observer 
at  H.  Then  H  m  E  is  the  parallax  of  a  body  m,  the  moon  for  example. 
As  TO  rises  higher  and  higher  in  the  heavens  to  the  points  m',  m",  &c., 
the  parallax  H  m'  E,  H  m"  E,  &c.  decreases.  At  Z,  the  zenith,  or  point 
immediately  above  the  head  of  the  observer,  it  is  zero;  and  at  m,  where 
the  body  is  in  the  horizon,  the  angle  H  m  E  is  the  greatest  possible,  and 
is  called  the  horizontal  parallax.  It  is  clear  that  with  regard  to  celestial 
bodies  the  whole  effect  of  parallax  is  in  the  vertical,  or  in  the  direction 
m  m'  Z ;  and  as  a  person  at  H  sees  m'  in  the  direction  H  m'  A,  when  it 
really  is  in  the  direction  E  m'  B,  it  makes  celestial  objects  appear  to  be 
lower  than  they  really  are.  The  distance  of  the  moon  from  the  earth 
has  been  determined  from  her  horizontal  parallax.  The  angle  E  m  H 
can  be  measured.  EH  m  is  a  right  angle,  and  EH,  the  radius  of  the 
earth,  is  known  in  miles ;  whence  the  distance  of  the  moon  E  m  is  easily 
found.  Annual  parallax  is  the  angle  under  which  the  diameter  of  the 
earth's  orbit  would  be  seen,  if  viewed  from  a  star. 

NOTE  129,  p.  52.— The  radii  n  B,  n  G,  &c.,  fig.  3,  are  equal  in  any  one 


412  NOTES. 

parallel  of  latitude,  A  a,  B  G ;  therefore  a  change  in  the  parallax  ob- 
served in  that  parallel  can  only  arise  from  a  change  in  the  moon's 
distance  from  the  earth :  and  when  tlie  moon  is  at  her  mean  distance, 
which  is  a  constant  quantity  equal  to  half  the  major  axis  of  her  orbit,  a 
change  in  the  parallax  observed  in  different  latitudes,  G  and  E,  must 
arise  from  the  difference  in  the  lengths  of  the  radii  n  G  and  C  E. 

NOTE  130,  p.  52.—  When  Venus  is  in  her  nodes.  She  must  be  in  the 
line  N  S  n,  where  her  orbit  P  N  A  n  cute  the  plane  of  the  ecliptic  E  N  e  n, 
fig.  12. 

NOTE  131,  p.  52.— -The  line  described,  $rc.     Let  E,  fig.  33,  be  the  earth, 


S  the  center  of  the  sun,  and  V  the  planet  Venus.  The  real  transit  of 
the  planet,  seen  from  E  the  center  of  the  earth,  would  be  in  the  direction 
A  B.  A  person  at  W  would  see  it  pass  over  the  sun  in  the  line  «  a,  and 
a  person  at  O  would  see  it  move  across  him  in  the  direction  v'  a'. 

NOTE  132,  p.  53. — Kepler's  law.  Suppose  it  were  required  to  find  the 
distance  of  Jupiter  from  the  sun.  The  periodic  times  of  Jupiter  and 
Venus  are  given  by  observation,  and  the  mean  distance  of  Venus  from 
the  center  of  the  sun  is  known  in  miles  or  terrestrial  radii ;  therefore,  by 
the  rule  of  three,  the  square  root  of  the  periodic  time  of  Venus  is  to  the 
square  root  of  the  periodic  time  of  Jupiter,  as  the  cube  root  of  the  mean 
distance  of  Venus  from  the  sun,  to  the  cube  root  of  the  mean  distance  of 
Jupiter  from  the  sun,  which  is  thus  obtained  in  miles  or  terrestrial  radii. 
The  root  of  a  number  is  that  number  which,  once  multiplied  by  itself, 
gives  its  square;  twice  multiplied  by  itself,  gives  its  cube,  &c.  For 
example,  twice  2  are  4,  and  twice  4  are  8  ;  2  is  therefore  the  square  root 
of  4,  and  the  cube  root  of  8.  In  the  same  manner  3  times  3  are  9,  and  3 
times  9  are  27  ;  Sis  therefore  the  square  root  of  9,  and  the  cube  root  of  27. 

NOTE  133,  p.  55. — Inversely,  <$-c.  The  quantities  of  matter  in  any  two 
primary  planets  are  greater  in  proportion  as  the  cubes  of  the  numbers 
representing  the  mean  distances  of  their  satellites  are  greater,  and  also  in 
proportion  as  the  squares  of  their  periodic  times  are  less. 

NOTE  134,  p.  55. — As  hardly  anything  appears  more  impossible  than 
that  man  should  have  been  able  to  weigh  the  sun  as  it  were  in  scales 
and  the  earth  in  a  balance,  the  method  of  doing  PO  may  have  some 
interest.  The  attraction  of  the  sun  is  to  the  attraction  of  the  earth,  as 
the  quantity  of  matter  in  the  sun  to  the  quantity  of  matter  in  the  earth : 
and  as  the  force  of  this  reciprocal  attraction  is  measured  by  its  effects, 
the  space  the  earth  would  fall  through  in  a  second  by  the  sun's  attrac- 
tion, is  to  the  space  which  the  sun  would  fall  through  by  the  earth's 
attraction,  as  the  mass  of  the  sun  to  the  mass  of  the  earth.  Hence,  as 
many  times  as  the  fall  of  the  earth  to  the  sun  in  a  second  exceeds  the 
fall  of  the  sun  to  the  earth  in  the  same  time,  so  many  times  does  the 
mass  of  the  sun  exceed  the  mass  of  the  earth.  Thus  the  weight  of  the 
sun  will  be  known  if  the  length  of  these  two  spaces  can  be  found  in 
miles  or  parts  of  R  mile.  Nothing  can  be  easier.  A  heavy  body  falls 
through  16-0697  feet  in  a  second  at  the  surface  of  the  earth  by  the 
earth's  attraction ;  and  as  the  force  of  gravity  is  inversely  as  the  square 


NOTES.  413 

of  the  distance,  it  is  clear  that  16-0697  feet  are  to  the  space  a  body  would 
fall  through  :it  the  distance  of  the  sun  by  the  earth's  attraction,  as  the 
square  nf  tlie  distance  of  the  sun  from  the  earth  to  the  square  of  the 
distance  of  the  center  of  the  earth  from  its  surface ;  that  is,  as  the  square 
<>t'i».i.(KM),OOU  miles  to  the  square  of  4000  miles.  And  thus,  by  a  simple 
question  in  the  rule  of  three,  the  space  which  the  sun  would  fall  through 
in  a  second  by  the  attraction  of  the  earth  may  be  found  in  parts  of  a 
mile.  The  space  the  earth  would  fall  through  in  a  second  by  the  attrac- 
tioa  of  the  sun  must  now  be  found  in  miles  also.  Suppose  m  x,  fig.  4,  to 
be  the  arc  which  the  earth  describes  round  the  sun  in  C  in  a  second  of 
time,  by  the  joint  action  of  the  sun  and  the  centrifugal  force.  By  the 
centrifugal  force  alone  the  earth  would  move  from  m  to  T  in  a  second, 
and  by  the  sun's  attraction  alone  it  would  fall  through  T  n  in  the  same 
time.  Hence  the  length  of  T  n  in  miles  is  the  space  the  earth  would  fall 
through  in  a  second  by  the  sun's  attraction.  Now  as  the  earth's  orbit  is 
very  nearly  a  circle,  if  360  degrees  be  divided  by  the  number  of  seconds 
in  a  sidereal  year  of  365$  days,  it  will  give  mn,  the  arc  which  the  earth 
moves  through  in  a  second,  and  then  the  tables  will  give  the  length  of 
the  line  TC  in  numbers  corresponding  to  that  angle;  but  as  the  radius 
C  it  is  assumed  to  be  unity  in  the  tables,  if  1  be  subtracted  from  the 
number  representing  CT,  the  length  of  Tre  wHl  be  obtained  ;  and  when 
multiplied  by  95,000,000  to  reduce  it  to  miles,  the  space  which  the  earth 
falls  through  by  the  sun's  attraction  will  be  obtained  in  miles.  By  this 
simple  process  it  is  found  that  if  the  sun  were  placed  in  one  scale  of  a 
balance,  it  would  require  354,936  earths  to  form  a  counterpoise. 

XOTE  135,  p.  58.  The  sum  of  the  greatest  and  least  distances,  S  P,  S  A, 
fis.  1-2,  is  equal  to  PA,  the  major  axis;  and  their  difference  is  equal  to 
twice  the  eccentricity  CS.  The  longitude  T  S  P  of  the  planet,  when  in 
the  point  P,  at  its  least  distance  from  the  sun,  is  the  longitude  of  the  peri- 
helion. The  greatest  height  of  the  planet  above  the  plane  of  the  ecliptic 
E  N  e  n  is  equal  to  the  inclination  of  the  orbit  P  N  A  n  to  that  plane.  The 
longitude  of  the  -planet,  when  in  the  plane  of  the  ecliptic,  can  only  be  the 
longitude  of  one  of  the  points  N  or  n ;  and  when  one  of  these  points  is 
known,  the  other  is  given,  being  180°  distant  from  it.  Lastly,  the  time 
included  between  two  consecutive  passages  of  the  planet  through  the 
same  node  N  or  n  is  its  periodic  time,  allowance  being  made  for  the  recess 
of  the  node  in  the  interval. 

NOTE  136,  p.  59.  Suppose  that  it  were  required  to  find  the  position  of 
a  point  in  space,  as  of  a  planet,  and  that  one  observation  places  it  in  n, 
fig.  34.  another  observation  places  it  in  n',  Fig.  34. 

another  hi  n",  and  so  on ;  all  the  points 
n,  ;t',  n",  n'",  &c.  being  very  near  to  one 
another.  The  true  place  of  the  planet  P 
will  not  differ  much  from  any  of  these 
positions.  It  is  evident,  from  this  view  of 
the  subject,  that  P  n,  P  «',  P  n",  &c.  are 
the  errors  of  observation.  The  true  posi- 
tion of  the  planet  P  is  found  by  this  prop- 
erty, that  the  squares  of  the  numbers 
representing  the  lines  P  n,  P  n',  &.C.,  when,  v» ., 
added  together,  are  the  least  possible. 
Each  line  P  n,  P  n',  &c.  being  the  whole  error  in  the  place  of  the  planet,  is 
made  up  of  the  errors  of  all  the  elements;  and  when  compared  with  the 
errors  obtained  from  theory,  it  affords  the  means  of  finding  each.  The 
principle  of  least  squares  is  of  very  general  application ;  its  demonstration 
cannot  find  a  place  here ;  but  the  reader  is  referred  to  Biot's  Astronomy, 
vol.  ii.  p.  203. 

NOTE  137,  p.  61.— An  axis   that,  Sre.    Fig.  20  represents   the   earth 

M  :i  a 


414  NOTES. 

revolving  in  its  orbit  about  the  sun  S,  the  axis  of  rotation  Pp  being  every- 
where parallel  to  itself. 

NOTE  138,  p.  61. — Angular  velocities  that  are  sensibly  uniform.  The 
earth  and  planets  revolve  about  their  axes  with  an  equable  motion,  which 
is  never  either  faster  or  slower.  For  example,  the  length  of  the  day  is 
never  more  nor  less  than  twenty-four  hours. 

NOTE  139,  p.  64.  If  fig.  1  be  the  moon,  her  polar  diameter  NS  is  the 
shortest;  and  of  those  in  the  plane  of  the  equator,  Q,Ey,  that  which 
points  to  the  earth  is  greater  than  all  the  others. 

NOTE  140,  p.  69. — Inversely  proportional,  &,-c.  That  is,  the  total  amount 
of  solar  radiation  becomes  less  as  the  minor  axis  C  C',  fig.  20,  of  the  earth's 
orbit  becomes  greater. 

NOTE  141,  p.  70.  Fig.  35  represents  the 
position  of  the  apparent  orbit  of  the  sun 
as  it  is  at  present,  the  earth  being  in  E. 
The  sun  is  nearer  to  the  earth  in  moving 
through  =^=P  T,  than  in  moving  through 
T  A:£=,  but  its  motion  through  =^P  T 
is  more  rapid  than  its  motion  through 
T  A  ^= ;  and  as  the  swiftness  of  the  mo- 
tion and  the  quantity  of  heat  received 
vary  in  the  same  proportion,  a  compensa- 
tion takes  place. 

NOTE  142,  p.  71.— In  an  ellipsoid  of  revolution,  fig.  1,  the  polar  diameter 
NS  and  every  diameter  in  the  equator  qlS>Q,e  are  permanent  axes  of 
rotation,  but  the  rotation  would  be  unstable  about  any  other.  Were  the 
earth  to  begin  to  rotate  about  C  a,  the  angular  distance  from  a  to  the  equa- 
tor at  q  would  no  longer  be  ninety  degrees,  which  would  be  immediately 
detected^ by  the  change  it  would  occasion  in  the  latitudes. 

NOTE  143,  pp.  50,  75.  Let  q  T  Q,,  and  E  T  e,  fig.  1 1,  be  the  planes  of  the 
equator  and  ecliptic.  The  angle  e  If  Q,,  which  separates  them,  called  the 
obliquity  of  the  ecliptic,  varies  in  consequence  of  the  action  of  the  sun 
and  moon  upon  the  protuberant  matter  at  the  earth's  equator.  That 
action  brings  the  point  Q  toward  e,  and  tends  to  make  the  plane  q  T  a 
coincide  with  the  ecliptic  E  T  e,  which  causes  the  equinoctial  points,  T 
and  =£:,  to  move  slowly  backward  on  the  plane  e  T  E  at  the  rate  of  50"'4l 
annually.  This  part  of  the  motion,  which  depends  upon  the  form  of  the 
earth,  is  called  luni-solar  precession.  Another  part,  totally  independent 
of  the  form  of  the  earth,  arises  from  the  mutual  action  of  the  earth, 
planets,  and  sun,  which,  altering  the  position  of  the  plane  of  the  ecliptic 
e  T  E,  causes  the  equinoctial  points  T  and  :£=  to  advance  at  the  rate  of 
0"-31  annually ;  but  as  this  motion  is  much  less  than  the  former,  the 
equinoctial  points  recede  on  the  plane  of  the  ecliptic  at  the  rate  of  50"'l 
annually.  This  motion  is  called  the  precession  of  the  equinoxes. 

NOTE  144,  pp.  61,  76.  Let  q  T  Q,,  e  T  E,  fig.  36,  be  the  planes  of  the 
equinoctial  or  celestial  equator  and  ecliptic,  and  p,  P,  their  poles.  Then 
suppose  p,  the  pole  of  the  equator,  to  revolve  with  a  tremulous  or  wavy 
motion  in  the  little  ellipse  pcdb  in  about  19  years,  both  motions  being 
very  small,  while  the  point  a  is  carried  round  in  the  circle  a  A  B  in  25,868 
years.  The  tremulous  motion  may  represent  the  half-yearly  variation, 
the  motion  in  the  ellipse  gives  an  idearfif  the  nutation  discovered  by  Brad- 
ley, and  the  motion  in  the  circle  a  A  B  arises  from  the  precession  of  the 
equinoxes.  The  greater  axis  pd  of  the  small  ellipse  is  18" -5,  its  minor 
axis  be  is  13"-74.  These  motions  are  so  small,  that  they  have  very  liltle 
effect  on  the  parallelism  of  the  axis  of  the  earth's  rotation  during  its  revo- 
lution round  the  sun,  as  represented  in -fig.  20.  As  the  stars  are  fixed,  this 


NOTES.  415 


real  motion  in  the  pole  of  the  earth  must  cause  an  apparent  change  in 
their  places. 

NOT*  145,  p.  78.  Let  N  be  the  pole,  fig.  11,  cE  the  ecliptic,  and  Q,q 
the  equator.  Then  N  n  m  S  being  a  meridian,  and  at  right  angles  to  the 
equator,  the  arc  T  m  is  less  than  the  arc  T  n. 

NOTE  146,  p.  80. — Heliacal  rising  of  Sirius.  When  the  star  appears 
in  the  morning,  in  the  horizon,  a  little  before  the  rising  of  the  sun. 

NOTK  147,  p.  82.  Let  P  T  A  ^  fig.  35,  be  the  apparent  orbit  or  path 
of  the  sun,  the  earth  being  in  E.  Its  major  axis,  A  P,  is  at  present  situate 
as  in  the  figure,  where  the  solar  perigee  P  is  between  the  solstice  of 
winter  and  the  equinox  of  spring.  So  that  the  time  of  the  sun's  passage 
through  the  arc  T  A  =£=  is  greater  than  the  time  he  takes  to  go  through 
the  arc  =2=  P  T .  The  major  axis  A  P  coincided  with  ^=  T,  the  line  of  the 
equinoxes,  4000  years  before  the  Christian  era ;  at  that  time  P  was  in  the 
point  T.  In  6468  of  the  Christian  era,  the  perigee  P  will  coincide  with 
=£=.  In  1234  A.  D.  the  major  axis  was  perpendicular  to  T  ^,  and  then  P 
was  in  the  winter  solstice. 

NOTE  148,  p.  83. — jit  the  solstices,  «$-c.  Since  the  declination  of  a  celes- 
tial object  is  its  angular  distance  from  the  equinoctial,  the  declination  of 
the  sun  at  the  solstice  is  equal  to  the  arc  Q  e,  fig.  11,  which  measures  the 
obliquity  of  the  ecliptic,  or  angular  distance  of  the  plane  T  e=£=  from  the 
plane  T  Q:£h. 

NOTE  149,  p.  83. — Zenith  distance  is  the  angular  distance  of  a  celestial 
object  from  the  point  immediately  over  the  head  of  an  observer. 

NOTE  150,  p.  84. — Reduced  to  the  lerel  of  the  sea.  The  force  of  gravita- 
tion decreases  as  the  square  of  the  height  above  the  surface  of  the  earth 
increases,  so  that  a  pendulum  vibrates  slower  on  high  ground ;  and  in 
order  to  have  a  standard  independent  of  local  circumstances,  it  is  neces- 
sary to  reduce  it  to  the  length  that  would  exactly  make  86,400  vibrations 
in  a  mean  solar  day  at  the  level  of  the  sea. 

NOTE  151,  p.  84. — A  quadrant  of  the  meridian  is  a  fourth  part  of  a 
meridian,  or  an  arc  of  a  meridian  containing  90°,  as  N  Q,  fig.  11. 

NOTE  152,  p.  86.—  The  angular  velocity  of  the  earth's  rotation  is  at  the 


416 


NOTES. 


rate  of  180°  in  twelve  hours,  which  is  the  time  included  between  the 
passages  .of  the  moon  at  the  upper  and  under  meridian. 

NOTE  153,  p.  99.— If  S  be  the  earth,  fig.  14,  d  the  sun,  and  C  Q,  O  D  the 
orbit  of  the  moon,  then  C  and  O  are  the  syzygies.  When  the  moon  is 
new  she  is  at  C,  and  when  full  she  is  at  O  ;  and  as  both  sun  and  moon 
are  then  on  the  same  meridian,  it  occasions  the  spring-tides,  it  being  high 
water  at  places  under  C  and  O,  while  it  is  low  water  at  those  under  a 
and  D.  The  neap-tides  happen  when  the  moon  is  in  quadrature  at  Q, 
or  D,  for  then  she  is  distant  from  the  sun  by  the  angle  dSQ,,  or  tfSD, 
each  of  which  is  90°. 

NOTE  154,  pp.  89,  90.— Declination.  If  the  earth  be  in  C,  fig.  11,  and 
if  q  T  Q,  be  the  equinoctial,  and  N  m  S  a  meridian,  then  in  C  n  is  the  de- 
clination of  a  body  at  n.  Therefore  the  cosine  of  that  angle  is  the  cosine 
of  the  declination. 

NOTE  155,  p.  91. — Moon  s  southing.  The  time  when  the  moon  is  on 
the  meridian  of  any  place,  which  happens  about  forty-eight  minutes  later 
every  day. 

NOTE  156,  pp.  93, 124.— Fig.  37  shows  the  propagation  of  waves  from 

Fig.  37. 


1  

C-  C' 

two  points  C  and  C',  where  stones  are  supposed  to  have  fallen.  Those 
points  in  which  the  waves  cross  each  other,  are  the  places  where  they 
counteract  each  other's  effects,  so  that  the  water  is  smooth  there,  while 
it  is  agitated  in  the  intermediate  spaces. 

NOTE  157,  p.  94.— The  centrifugal  force  may,  8,-c.  The  centrifugal 
force  acts  in  a  direction  at  right  angles  to  N  S,  the  axis  of  rotation,  fig.  30. 
Its  effects  are  equivalent  to  two  forces,  one  of  which  is  in  the  direction 
bm  perpendicular  to  the  surface  Q,m?t  of  the  earth,  and  diminishes  the 
force  of  gravity  at  m.  The  other  acts  in  the  direction  of  the  tangent  mT, 
which  makes  the  fluid  particles  tend  toward  the  equator. 

NOTE  158,  p.  101. — Analytical  formula  or  expression.  A  combination 
of  symbols  or  signs  expressing  or  representing  a  series  of  calculation,  and 
including  every  particular  case  that  can  arise  from  a  general  law. 

NOTE  159,  p.  104.— Platina.  The  heaviest  of  metals;  its  color  is  be- 
;  of  silv* 


tween  that 


ver  and  lead. 


NOTE  160,  p.  105.— Fig.  38  is  a  perfect  octahedron.     Sometimes  !ts  an- 
gles, A,X,  a,  a,  &c.,  are  truncated,  or  cut  off.    Sometimes  a  slice  is  cut 


NOTES. 


417 


off  its  edges  A  a,  X  a,  a  a,  &c.   Occasionally  both  these  modifications  take 
place. 

Fig.  38. 


NOTE  161,  p.  106.  —  Prismatic  crystals  of  sulphate  of  nickel  are  some- 
what like  fig.  62,  only  that  they  are  thin,  like  a  hair. 

NOTE  162,  p.  106.  —  Zinc,  a  metal  either  found  as  an  ore  or  mixed 
with  other  metals.    It  is  used  in  making  brass. 

C 


NOTE  163,  p.  107. — A  cube  is  a  solid 
contained  by  six  plane  square  surfaces, 
as  fig.  39. 


Fig.  40. 


NOTE  164,  p.  107. — A  tetrahedron  is  a  solid  contained  by  four  triangular 
surfaces,  as  fig.  40 :  of  this  solid  there  are  many  varieties. 

NOTE  165,  p.  107.  — There  are  many  varieties  of  the  octahedron.  In 
that  mentioned  in  the  text,  the  base  a  a  a  a,  fig.  38,  is  a  square,  but  the 
base  may  be  a  rhomb  ;  this  solid  may  also  be  elongated  in  the  direction 
of  its  axis  A  X,  or  it  may  be  depressed. 

NOTE  166,  pp.  108, 186.  —  A  rhombohedron  is  a  solid  contained  by  six 
plane  surfaces,  as  in  fig.  63,  the  opposite  planes  being  equal  and  similar 
rhombs  parallel  to  one  another;  but  all  the  planes  are  not  necessarily 
equal  or  similar,  nor  are  its  angles  right  angles.  In  carbonate  of  lime  the 
angle  C  A  B  is  105°-55,  and  the  angle  B  or  C  is  75°-05. 

NOTE  167,  p.  108.  —  Sublimation.  Bodies  raised  into  vapor  which  W 
again  condensed  into  a  solid  state. 

NOTE  168,  p.  109.  — The  surface  of  a 
column  of  water,  or  spirit  of  wine,  in  a 
capillary  tube,  ie  hollow ;  and  that  of  a 
column  of  quicksilver  is  convex,  or  round- 
ed, as  in  fig.  41. 

27 


418 


NOTES. 


NOTK  169,  p.  109.— Inverse  ratio,  &c.  The  elevation  of  the  liquid  is 
greater  in  proportion  as  the  internal  diameter  of  the  tube  is  less. 

NOTE  170,  p.  110. — In  fig.  41,  the  line  cd  shows  the  direction  of  the 
resulting  force  in  the  two  cases. 

NOTE  171,  p.  110. — When  two  plates  of  glass  are  brought  near  to  one 
another  in  water,  the  liquid  rises  between  them ;  and  if  the  plates  touch 
each  other  at  one  of  their  upright  edges,  the  outline  of  the  water  will  be- 
come a  hyperbola. 

NOTE  172,  p.  111. —Let  A  A',  fig.  42,  be  two  plates,  both  of  which  are 
fet,  and  B  B',  two  that  are  dry.  When  partly  immersed  in  a  liquid,  its 


wet, 


Fig.  42. 


surface  will  be  curved  close  to  them,  but  will  be  of  its  usual  level  for  the 
rest  of  the  distance.  At  such  a  distance,  they  will  neither  attract  nor 
repel  one  another.  But  as  soon  as  they  are  brought  near  enough  to  have 
the  whole  of  the  liquid  surface  between  them  curved,  as  in  a  a',  b  b',  they 
will  rush  together.  If  one  be  wet  and  another  dry,  as  C  C',  they  will 
repel  one  another  at  a  certain  distance ;  but  as  soon  as  they  are  brought 
very  near,  they  will  rush  together,  as  in  the  former  cases. 

NOTE  173,  p.  128. — Latent  heat.  There  is  a  certain  quantity  of  heat 
in  all  bodies,  which  cannot  be  detected  by  the  thermometer,  but  which 
may  become  sensible  by  compression. 

NOTE  174,  p.  131. — Reflected  waves.     A  series  of  waves  of  light,  sound, 


Fif.  43. 


NOTES. 


419 


or  water,  diverge  in  all  directions  from  their  origin  I,  fig.  43,  as  from  a 
center.  When  they  meet  with  an  obstacle  8  S,  they  strike  ngainst  it, 
and  are  reflected  or  turned  back  by  it  in  the  same  form,  as  if  they  had 
proceeded  from  the  center  C,  at  an  equal  distance  on  the  other  side  of 
the  surface  SS. 

NOTE  175,  p.  132.— Elliptical  shell.  If  fig.  6  be  a  section  of  an  ellip- 
tical shell,  then  all  sounds  coming  from  the  focus  S  to  different  points 
on  the  surface,  as  TO,  are  reflected  back  to  F,  because  the  angle  T  m  8 
is  equal  to  imF.  In  a  spherical  hollow  shell,  a  sound  diverging  from 
the  center  is  reflected  back  to  the  center  again. 

NOTE  176,  p.  136.  Fig.  44  represents  musical  strings  in  vibration ;  the 
Fig.  44. 


straight  lines  are  the  strings  when  at  rest.  The  first  figure  of  the  four 
would  give  the  fundamental  note,  as,  for  example,  the  low  C.  The 
second  and  third  figures  would  give  the  first  and  second  harmonics ;  that 
is,  the  octave  and  the  12th  above  C,  nnn  being  the  points  of  rest;  the 
fourth  figure  shows  the  real  motion  when  compounded  of  all  three. 

NOTE  177,  p.  137.    Fig.  45  represents  sections  of  an  open  and  of  a  shut 
pipe,  and  of  a  pipe  open  at  one  end.    When  sounded,  the  air  sponta- 
sly  divides  itself  into  segments. .  It  remains  at  rest  in  the  divisions 


or  nodes  nn'.&c.,  but  vibrates  between  them  in  the  direction  of  the 
arrow-heads.  The  undulations  of  the  whole  column  of  air  give  the 
fundamental  note,  while  the  vibrations  of  the  'divisions  give  the  har- 
monics. 

NOTE  178,  p.  139.  Fig.  1,  plate  1,  shows  the  vibrating  surface  when 
the  sand  divides  it  into  squares,  and  fig.  2  represents  the  same  when  the 
nodal  lines  divide  it  into  triangles.  The  portions  marked  a  a  are  in 
different  states  of  vibration  from  those  marked  b  b. 


420 


NOTES. 


NOTE  179,  p.  140.  Plates  1  and  2  contain  a  few  of  Chladnl's  figures. 
The  white  lines  are  the  forms  assumed  by  the  sand,  from  different  modes 
of  vibration,  corresponding  to  musical  notes  of  different  degrees  of  pitch. 
Plate  3  contains  six  of  Chladni's  circular  figures. 

NOTE  180,  p.  140.  Mr.  Wheatstone's  principle  is,  that  when  vibra- 
tions producing  the  forms  of  figs.  1  and  2,  plate  3,  are  united  in  the  same 
surface,  they  make  the  sand  assume  the  form  of  fig.  3.  In  the  same 
manner,  the  vibrations  which  would  separately  cause  the  sand  to  take 
the  forms  of  figs.  4  and  5,  would  make  it  assume  the  form  of  fig.  6  when 
united.  The  figure  9  results  from  the  modes  of  vibration  of  7  and  8 
combined.  The  parts  marked  a  a  are  in  different  states  of  vibration  from 
those  marked  b  b.  Figs.  1,  2,  and  3,  plate  4,  represent  forms  which  the 
sand  takes  in  consequence  of  simple  modes  of  vibration ;  4  and  5  are 
those  arising  from  two  combined  modes  of  vibration  ;  and  the  last  six 
figures  arise  from  four  superimposed  simple  modes  of  vibration.  These 
complicated  figures  are  determined  by  computation  independent  of  experi- 
ment. 

NOTE  181,  p.  140.— The  long  cross-lines  of  fig.  46  show  the  two  sys- 
tems of  nodal  lines  given  by  M.  Savart's  laminae. 

]Fig.  46. 


LLLU1 


ilLLJ 


NOTE  182,  p.  141.— The  short  lines  on  fig.  46  show  the  positions  of  the 
nodal  lines  on  the  other  sides  of  the  same  laminae. 

NOTE  183,  p.  141.— Fig.  47  gives  the  nodal  lines  on  a  cylinder,  with  the 
paper  rings  that  mark  the  quiescent  points. 

Fiff.  47. 


NOTE  184,  pp.  133,  148,  149.— Reflection  and  refraction.     Let  P  C  p, 


Fig.  48. 


fig.  48,  be  perpendicular  to  a  sur- 
face of  glass  or  water  A  B.  When 
a  ray  of  light,  passing  through  the 
air,  falls  on  this  surface  in  any  di- 
rection I  C,  part  of  it  is  reflected 
in  the  direction  C  S,  and  the  oth 
er  part  is  bent  at  C,  and  passes 
through  the  glass  or  water  in  the 
direction  CR.  1C  is  called  the 
incident  ray,  and  ICP  the  angle 
of  incidence  ;  C  S  is  the  reflected 
ray,  and  P  C  S  the  angle  of  reflec- 
tion :  C  R  is  the  refracted  ray,  and 
p  C  R  the  angle  of  refraction.  The 
plane  passing  through  S  C  and  1 C 
is  the  plane  of  reflection,  and  the 
plane  passing  through  1C  and  C  R 
is  the  plane  of  refraction.  In  or 
dinary  cases,  C  I,  C  S,  C  B,  are  all 


NOTES. 


421 


in  the  same  plane.  We  see  the  surface  by  means  of  the  reflected  light, 
which  would  otherwise  be  invisible.  Whatever  the  reflecting  surface  may 
be,  and  however  obliquely  the  light  may  fall  upon  it.  the  angle  of  reflection 
is  always  equal  to  the  angle  of  incidence.  Thus  1C,  1'  C,  being  rays  in- 
cident on  the  surface  at  C,  they  will  be  reflected  into  CS,  C  S',  so  that 
the  angle  8  C  P  will  be  equal  to  the  angle  I  C  P,  and  S'  Cf  equal  to  I'  C  P. 
That  is  by  no  means  the  case  with  the  refracted  rays.  The  incident 
rays  I  C,  I'  C,  are  bent  at  C,  toward  the  perpendicular,  in  the  direction 
CR,  CR' ;  and  the  law  of  refraction  is  such,  that  the  sine  of  the  angle 
of  incidence  has  a  constant  ratio  to  the  sine  of  the  angle  of  refraction  ; 
that  is  to  say,  the  number  expressing  the  length  of  I  m.  the  sine  of  I  C  P, 
divided  by  the  number  expressing  the  length  of  R  n,  the  sine  of  RC/>,  is 
the  same  for  all  the  rays  of  light  that  can  fall  upon  the  surface  of  any  one 
substance,  and  is  called  its  Index  of  refraction.  Though  the  index  of  re- 
fraction be  the  same  for  any  one  substance,  it  is  not  the  same  for  all  sub- 
stances. For  water  it  is  1-336 ;  for  crown-glass  it  is  1-535  ;  for  flint-glass, 
1-6;  for  diamond,  2-487;  and  for  chromate  of  lead  it  is  3,  which  sub- 
stance has  a  higher  refractive  power  than  any  other  known.  Light  fall- 
ing perpendicularly  on  a  surface,  passes  through  it  without  being  refract- 
ed. If  the  light  be  now  supposed  to  pass  from  a  dense  into  a  rare  medium, 
as  from  glass  or  water  into  air,  then  RC,  R'  C,  become  the  incident  rays ; 
and  in  this  case  the  refracted  rays,  C  I,  C  I'  are  bent  from  the  perpendic- 
ular instead  of  toward  it.  When  the  incidence  is  very  oblique,  as  rC, 
the  light  never  passes  into  the  air  at  all,  but  it  is  totally  reflected  in  the 
direction  C  r'.  so  that  the  angle  p  C  r  is  equal  to  p  C  r' :  that  frequently 
happens  at  the  second  surface  of  glass.  When  a  ray  1C  falls  from  air 
upon  a  piece  of  glass  A  B,  it  is  in  general  refracted  at  each  surface.  At 
C  it  is  bent  toward  the  perpendicular,  and  at  R  from  it,  and  the 'ray 
emerges  parallel  to  1C  ;  but  when  the  ray  is  very  oblique  to  the  second 
surface,  it  is  totally  reflected.  An  object  seen  by  total  reflection  is  nearly 
as  vivid  as  when  seen  by  direct  vision,  because  no  part  of  the  light  is  re- 
fracted. 

NOT«  185,  p.  148.— Atmospheric  rtfraction.    Let  a  ft,  a  *,  Ac.,  flg.  49,  be 
strata,  or  extremely  thin  layers,  of  the  atmosphere,  which  increase  in  den- 


rity  toward  win,  the  surface  of  the  earth.  A  ray  coming  from  a  star 
meeting  the  surface  of  the  atmosphere  at  8,  would  be  refracted  at  the 
surface  of  each  layer,  and  would  consequently  move  in  the  curved  line 
Bvv  v  A  ;  and  as  an  object  is  seen  in  the  direction  of  the  ray  that  meets 
the  eye,  the  star,  which  really  is  in  the  direction  AS,  would  seem  to  a 
NN 


422 


NOTES. 


person  at  A  to  be  in  s.  So  that  refraction,  which  always  acts  in  a  verti- 
cal direction,  raises  objects  above  their  true  place.  For  that  reason,  a 
body  at  S',  below  the  horizon  H  AO,  would  be  raised,  and  would  be  seen 
in  s'.  The  sun  is  frequently  visible  by  refraction  after  he  is  set,  or  before 
he  is  risen.  There  is  no  refraction  in  the  zenith  at  Z.  It  increases  all 
the  way  to  the  horizon,  where  it  is  greatest,  the  variation  being  propor- 
tional to  the  tangent  of  the  angles  ZAS,  ZAS',  the  distances  of  the 
bodies  S  S'  from  the  zenith.  The  more  obliquely  the  rays  fall  the  greater 
the  refraction. 

NOTE  186,  p.  149. — Bradley' s  method  of  ascertaining  the  amount  of  re- 
fraction.   Let  Z,  fig.  50,  be  the  zenith  or  point  immediately  above  an 
Fiff.  50. 


observer  at  A  ;  let  H  O  be  his  horizon,  and  P  the  pole  of  the  equinoctial 
A  a.  Hence  P  A  a  is  a  right  angle.  A  star  as  near  to  the  pole  as  * 
would  appear  to  revolve  about  it,  in  consequence  of  the  rotation  of  the 
earth.  At  noon,  for  example,  it  would  be  at  s  above  the  pole,  and  at 
midnight  it  would  be  in  s'  below  it.  The  sum  of  the  true  zenith 
distances  Z  A  s,  Z  A  s',  is  equal  to  twice  the  angle  ZAP.  Again,  S  and 
S'  being  the  sun  at  his  greatest  distances  from  the  equinoctial  A  Q,  when 
in  the  solstices,  the  sum  of  his  true  zenith  distances,  Z  A  S,  Z  A  S',  is 
equal  to  twice  the  angle  Z  A  Q.  Consequently,  the  four  true  zenith 
distances,  when  added  together,  are  equal  to  twice  the  right  angle  Q,  A  P; 
that  is,  they  are  equal  to  180°.  But  the  observed  or  apparent  zenith 
distances  are  less  than  the  true,  on  account  of  refraction ;  therefore  the 
sum  of  the  four  apparent  zenith  distances  is  less  than  180°  by  the  whole 
amount  of  the  four  refractions. 

NOTE  187,  p.  150. —  Terrestrial  refraction.  Let  C,  fig.  51,  be  the 
center  of  the  earth,  A  an  observer  at  its  surface,  A  H  his  horizon,  and 
B  some  distant  point,  as  the  top  of  a  hill.  Let  the  arc  B  A  be  the  path 
of  a  ray  coining  from  B  to  A  ;  E  B,  E  A,  tangents  to  its  extremities; 
and  A  G,  B  F,  perpendicular  to  C  B.  However  high  the  hill  B  may  be, 
it  is  nothing  when  compared  with  C  A,  the  radius  of  the  earth  ;  conse- 
quently, A  B  differs  so  little  from  A  D  that  the  angles  A  E  B  and 
ACB  are  supplementary  to  one  another;  that  is,  the  two  taken  together 
are  equal  to  180°.  A  C  B  is  called  the  horizontal  angle.  Now  BAH 
is  the  real  height  of  B,  and  E  A  H  its  apparent  height';  hence  refraction 
raises  the  object  B,  by  the  angle  E  A  B,  above  its  real  place.  Again, 
the  real  depression  of  A,  when  viewed  from  B.  is  F  B  A,  whereas 
its  apparent  depression  is  F  B  E,  so  E  B  A  is  due  to  refraction.  The 
angle  F  B  A  is  equal  to  the  sum  of  the  angles  BAH  and  ACB;  that 
is,  the  true  elevation  is  equal  to  the  true  depression  nnd  the  hori/ontM 


Fig.  51. 


423 


angle.  But  the  true  elevation  is  equal  to  the  apparent  elevation  dimin- 
ished by  the  refraction;  and  the  true  depression  is  equal  to  the  ap- 
parent depression  increased  by  refraction.  Hence  twice  the  refraction 
is  equal  to  the  horizontal  angle  augmented  by  the  difference  between  the 
apparent  elevation  and  the  apparent  depression. 

NOTE  188,  p.  151.    Fig.  52  represents  the  phenomenon  in  question.    SP 
is  the  real  ship,  with  its  inverted  and  direct  images  seen  in  the  air. 


Were  there  no  refraction,  the  rays  would  come  from  the  ship  S  P  to  the 
eye  E  in  the  direction  of  the  straight  lines ;  but,  on  account  of  the  variable 
density  of  the  inferior  strata  of  the  atmosphere,  the  rays  are  bent  in  the 
curved  lines  PcE,  PdE,  SmE,  SnE.  Since  an  object  is  seen  in  the 
direction  of  the  tangent  to  that  point  of  the  ray  which  meets  the  eye, 
the  point  P  of  the  real  ship  is  seen  at  p  and  p\  and  the  point  S  seems  to 
be  in  s  and  s' ;  and  as  all  the  other  points  are  transferred  in  the  same 
manner,  direct  and  inverted  images  of  the  ship  are  formed  hi  the  air 
above  it. 


424 


NOTES. 


Fig.  53. 


NOTE  189,  p.  151.  Fig.  53  represents  the  /  ; 
section  of  a  poker,  with  the  refraction  pro-  ;  / 
duced  by  the  hot  air  surrounding  it. 


NOTE  190,  p.  153.— The  solar  spectrum.    A  ray  from  the  sun  at  S,  fig. 
54,  admitted  into  a  dark  room  through  a  small  round  hole  H  in  a  vvindow- 


TOxkte 


shutter,  proceeds  in  a  straight  line  to  a  screen  D,  on  which  it  forms  a 
bright  circular  spot  of  white  light  of  nearly  the  same  diameter  with  the 
hole  H.  But  when  the  refracting  angle  B  A  C  of  a  glass  prism  is  inter- 
posed, so  that  the  sunbeam  falls  on  A  C  the  first  surface  of  the  prism,  and 
emerges  from  the  second  surface  A  B  at  equal  angles,  it  causes  the  rays 
to  deviate  from  the  straight  path  S  D,  and  bends  them  to  the  screen  M  N, 
where  they  form  a  colored  image  VR  of  the  sun,  of  the  same  breadth 
with  the  diameter  of  the  hole  H,  but  much  longer.  The  space  V  R  con- 
sists of  seven  colors, — violet,  indigo,  blue,  green,  yellow,  orange,  and  red. 
The  violet  and  red,  being  the  most  and  less  refrangible  rays,  are  at  the 
extremities,  and  the  green  occupy  the  middle  part  at  G.  The  angle  D  g  G 
is  called  the  mean  deviation,  and  the  spreading  of  the  colored  rays  over 
the  angle  V  g  R  the  dispersion.  The  deviation  and  dispersion  vary  with 
the  refracting  angle  B  A  C  of  the  prism,  and  with  the  substance  of  which 
it  is  made. 

NOTE  191,  p.  159.  Under  the  same  circumstances,  and  where  the  re- 
fracting angles  of  the  two  prisms  are  equal,  the  angles  D^G  and  \ g  R, 
fig.  54,  are  greater  for  flint-glass  than  for  crown-glass.  But  as  they  vary 
with  the  angle  of  the  prism,  it  is  only  necessary  to  augment  the  refracting 
angle  of  the  crown-glass  prism  by  a  certain  quantity,  to  produce  nearly 
the  same  deviation  and  dispersion  with  the  flint-glass  prism.  Hence, 


NOTES. 


425 


when  the  two  prisms  are  placed  with  their  refracting  angles  in  opposite 
directions,  as  in  fig.  54,  they  nearly  neutralize  each  other's  effects,  and 
refract  a  beam  of  light  without  resolving  it  into  its  elementary  colored 
rays.  Sir  David  Brewster  has  come  to  the  conclusion,  that  there  may  be 
refraction  without  color  by  means  of  two  prisms,  or  two  lenses,  when 
properly  adjusted,  even  though  they  be  made  of  the  same  kind  of  glass. 


KOTS  192,  p.  159.  — The  object  glass  of  the  achromatic 
telescope  consists  of  a  convex  lens  A  B,  fig.  55,  of  crown-glass, 
placed  on  the  outside  toward  the  object,  and  of  a  concavo- 
convex  lens  C  D  of  flint-glass  placed  toward  the  eye.  The 
focal  length  of  a  lens  is  the  distance  of  its  center  from  the 
point  in  which  the  rays  converge,  as  F,  fig.  60.  If,  then,  the 
lenses  A  B  and  CD  be  so  constructed  that  their  focal  lengths 
are  in  the  same  proportion  as  their  dispersive  powers,  they 
will  refract  rays  of  light  without  color. 


NOTE  193,  p.  162.— When  a  sunbeam,  after  having  passed  through  a 

Fig.  56. 

JVjr.57. 


colored  glass  V  V,  fig.  56,  enters  a  dark  room  by  two  small  slit*  OCX  in 
a  card,  or  piece  of  tin,  they  produce  alternate  bright  and  black  bands  on 


426 


NOTES. 


Fig.  58. 


a  screen  S  S'  at  a  little  distance.  When  either  one  or  other  of  the  slits 
O  or  O'  is  stopped,  the  dark  bands  vanish,  and  the  screen  is  illuminated 
by  a  uniform  light,  proving  that  the  dark  bands  are  produced  by  the  in- 
terference of  the  two  sets  of  rays.  Again,  let  H  m,  fig.  57,  be  a  beam  of 
white  light  passing  through  a  hold  at  H,  made  with  a  fine  needle  in  a 
piece  of  lead  or  a  card,  and  received  on  a  screen  S  S'.  When  a  hair,  or 
a  small  slip  of  card  hh'  about  the  30th  of  an  inch  in  breadth,  is  held  in 
the  beam,  the  rays  bend  round  on  each  side  of  it,  and,  arriving  at  the 
screen  in  different  states  of  vibration,  interfere  and  form  a  series  of  co- 
lored fringes  on  each  side  of  a  central  white  band  m.  When  a  piece  of 
card  is  interposed  at  C,  so  as  to  intercept  the  light  which  passes  on  one 
side  of  the  hair,  the  colored  fringes  vanish.  When  homogeneous  light 
>s  used,  the  fringes  are  broadest  in  red,  and  become  narrower  for  each 
color  of  the  spectrum  progressively  to  the  violet,  which  gives  the  nar- 
rowest and  most  crowded  fringes.  These  very  elegant  experiments  are 
due  to  Df.  Thomas  Young. 

NOTE  194,  pp.  165,  191.— Fig.  58  shows  Newton's  rings,  of  which  there 
are  seven,  formed  by  screwing  two  lenses  of 
glass  together.    Provided  the  incident  light  be 
white,  they  always  succeed  each  other  in  the 
following  order: 

1st  ring,  or  first  order  of  colors :  Black,  very 
faint  blue,  brilliant  white,  yellow,  orange,  red. 

2d  ring:  Dark  purple,  or  rather  violet,  blue, 
a  very  imperfect  yellow  green,  vivid  yellow, 
crimson  red. 

3d  ring  :  Purple,  blue,  rich  grass  green,  fine 
yellow,  pink,  crimson. 

4th  ring  :  Dull  bluish  green,  pale  yellowish  pink,  red. 

5th  ring:  Pale  bluish  green,  white,  pink. 

6th  ring :  Pale  blue-green,  pale  pink. 

7th  ring  :  Very  pale  bluish  green,  very  pale  pink. 

After  the  seventh  order,  the  colors  become  too  faint  to  be  distinguished. 
The  rings  decrease  in  breadth,  and  the  colors  become  more  crowded  to- 
gether, as  they  recede  from  the  center.  When  the  light  is  homogeneous, 
the  rings  are  broadest  in  the  red,  and  decrease  in  breadth  with  every 
successive  color  of  the  spectrum  to  the  violet. 

NOTE  195,  p.  166.  — The  absolute 
thickness  of  the  film  of  air  between 
the  glasses  is  found  as  follows : — Let 
A  F  B  C,  fig.  59,  be  the  section  of  a 
lens  lying  on  a  plane  surface  or  plate 
of  glass  PP',  seen  edgewise,  and  let 
E  C  be  the  diameter  of  the  sphere  of 
which  the  lens  is  a  segment.  If  A  B 
be  the  diameter  of  any  one  of  Newton's 
rings,  and  B  D  parallel  to  C  E,  then  B 
D  or  CF  is  the  thickness  of  the  air 
producing  it.  E  C  is  a  known  quanti- 
ty, and  when  AB  the  diameter  is 
measured  with  compasses,  B  D  or  F  C 
can  be  computed.  Newton  found  that 
the  length  of  B  D  corresponding  to  the 
darkest  part  of  the  first  ring,  is  the 
98,000th  part  of  an  inch  when  the  rays  fall  perpendicularly  on  the  lens, 
and  from  this  he  deduced  the  thickness  corresponding  to  each  color  in  the 
system  of  rings.  By  passing  each  color  of  the  solar  spectrum  in  succes- 
sion over  the  lenses,  Newton  also  determined  the  thickness  of  the  film 


NOTES. 


427 


of  air  corresponding  to  each  color,  from  the  breadth  of  the  rings,  which 
are  always  of  the  same  color  with  the  homogeneous  light. 

NOTE  196,  p.  168.— The  focal  length  or  distance 
of  a  lens  is  the  distance  from  its  center  to  the  point 
F,  fig.  60,  in  which  the  refracted  rays  meet.  Let 
L  L'  be  a  lens  of  very  short  focal  distance  fixed  in 
the  window-shutter  of  a  dark  room.  A  sunbeam 
S  L  L',  passing  through  the  lens,  will  be  brought 
to  a  focus  in  F,  whence  it  will  diverge  in  lines 
PC,  FD,and  will  form  a  circular  image  of  light 
on  the  opposite  wall.  Suppose  a  sheet  of  lead, 
having  a  small  pin-hole  pierced  through  it,  to  be 
placed  in  this  beam  ;  when  the  pin-hole  is  viewed 
from  behind  with  a  lens  at  E,  it  is  surrounded  with 
a  series  of  colored  rings,  which  vary  in  appear- 
ance with  the  relative  positions  of  the  pin-hole 
and  eye  with  regard  to  the  point  F.  When  the 
hole  is  the  30th  of  an  inch  in  diameter  and  at  the 
distance  of  6A  feet  from  F,  when  viewed  at  the 
distance  of  24  inches,  there  are  seven  rings  of  the 
following  colors : — 

1st  order:  White,  pale  yellow,  yellow,  orange, 
dull  red. 

2d  order :  Violet,  blue,  whitish,  greenish  yellow, 
fine  yellow,  orange  red. 

3d  order:  Purple,  indigo,  blue,  greenish  blue, 
brilliant  green,  yellow  green,  red. 

4th  order  :  Good  green,  bluish  white,  red. 

5th  order:  Dull  green,  faint  bluish  white,  faint 
red. 

6ih  order :  Very  faint  green,  very  faint  red. 

7th  order :  A  trace  of  green  and  red. 


NOTI  197.  p.  168.— Let  LL',  fig.  61, 
be  the  section  of  a  lens  placed  in  a 
window-shutter,  through  which  a  very 
small  beam  of  light  S  L  L'  passes  into 
a  dark  room,  and  comes  to  a  focus  in  F. 
If  the  edge  of  a  knife  KN  be  held  in 
the  beam,  the  rays  bend  away  from  it 
in  hyperbolic  curves  K  r,  K  r',  &c.  in- 
stead of  coming  directly  to  the  screen 
in  the  straight  line  K  E",  which  is  the 
boundary  of  the  shadow.  As  these 
bending  rays  arr.ve  at  the  screen  indif- 
ferent states  of  undulation,  they  inter- 
fere, and  form  a  series  of  colored  fringes, 
rrj.  &.c.  along  the  edge  of  the  shadow 
K  E  S  X  of  the  knife.  The  fringes  vary 
in  breadth  with  the  relative  distances 
of  the  knife  edge  and  screen  from  F. 


428 


NOTES. 


NOTE  198,  p.  171.  Fig.  43  represents  the  phenomeaa  in  question,  where 
S  S  is  the  surface,  and  I  the  center  of  incident  waves.  The  reflected 
waves  are  the  dark  lines  returning  toward  I,  which  are  the  same  as  if 
they  had  originated  in  C  on  the  other  side  of  the  surface. 

NOTE  199,  p.  173.  Fig.  62  represents  a  prismatic  crystal  of  tourma- 
line, whose  axis  is  A  X.  The  slices  that  are  used  for  polarizing  light  are 
cut  parallel  to  AX. 

Fig.  62.  Fig.  63. 

A 


NOTE  200,  p.  175,-Double  refraction.  If  a  pencil  of  light,  Rr,  fig.  63, 
fa-Us  upon  a  rhombohedron  of  Iceland  spar,  A  B  X  C,  it  is  separated  into 
two  equal  pencils  of  light  at  r,  which  are  refracted  in  the  directions  rO, 
r  E :  when  these  arrive  at  O  a-nd  E  they  are  again  refracted,  and  pass 
into  the  air  in  the  directions  Oo,  Eo,  parallel  to  one  another  and  to  the 
incident  ray  Rr.  The  ray  rO  is  refracted  according  to  the  ordinary  law, 
which  is,  that  the  sines  of  the  angles  of  incidence  and  refraction  bear  a 
constant  ratio  to  one  another  (see  Note  184),  and  the  rays  Rr,  rO,  Oo 
are  all  in  the  same  plane.  The  pencil  rE,  on  the  contrary,  is  bent  aside 
out  of  that  plane,  and  its  refraction  does  not  follow  the  constant  ratio 
of  the  sines;  rE  is  therefore  called  the  extraordinary  ray,  and  rO  the 
ordinary  ray.  In  consequence  of  this  bisection  of  the  light,  a  spot  of  ink  at 
O  is  seen  double  at  O  and  E,  when  viewed  from  r  ;  and  when  the  crystal 
is  turned  round,  the  image  E  revolves  about  O,  which  remains  stationary. 

NOTE  201,  p.  176.  Both  of  the  parallel  rays  Oo  and  Eo,  fig.  63,  are 
polarized  on  leaving  the  doubly  refracting  crystal,  and  in  both  the  parti- 
cles of  light  make  their  vibrations  at  right  angles  to  the  lines  Oo  Eo. 
In  the  one,  however,  these  vibrations  lie,  for  example,  in  the  plane  of  the 
horizon,  while  the  vibrations  of  the  other  lie  in  the  vertical  plane  per- 
pendicular to  the  horizon. 

NOTE  202,  p.  177.  If  light  be  made  to  fall  in  various  directions  on  the 
natural  faces  of  a  crystal  of  Iceland  spar,  or  on  faces  cut  and  polished 
artificially,  one  direction,  A  X,  fig.  63,  will  be  found,  along  which  the 
light  passes  without  being  separated  into  two  pencils.  A  X  is  the  optic 
axis.  In  some  substances  there  are  two  optic  axes  forming  an  angle  with 
each  other.  The  optic  axis  is  not  a  fixed  line,  it  only  has  a  fixed  direc- 
tion ;  for  if  a  crystal  of  Iceland  spar  be  divided  into  smaller  crystals,  each 
will  have  its  optic  axis ;  but  if  all  these  pieces  be  put  together  again,  their 
optic  axes  will  be  parallel  to  A  X.  Every  line,  therefore,  within  the 
crystal  parallel  to  AX  is  an  optic  axis;  but  as  these  lines  have  all  the 
same  direction,  the  crystal  is  still  said  to  have  but  one  optic  axis. 

NOTE  203.  p.  178.     If  1C,  fig.  48,  be  the  incident  and  CS  the  reflected 


NOTES. 


429 


rays,  then  the  particles  of  polarized  light  make  their  vibrations  at  right 
angles  to  the  plane  of  the  paper. 

NOTE  904,  p.  178.  Let  A  B.  fig.  48,  be  the  surface  of  the  reflector,  1C 
the  incident,  and  CS  the  reflected  rays;  then,  when  the  angle  SCB  is 
57°,  and  consequently  the  angle  PCS  equal  to  33°,  the  black  spot  will 
be  seen  at  C  by  an  eye  at  S. 

NOTE  205,  p.  179.  Let  A  B,  fig.  48,  be  a  reflecting  surface.  I C  the  inci- 
dent, and  CS  the  reflected  rays;  then,  if  the  surface  be  plate-glass,  the 
angle  SCB  must  be  57°,  in  order  that  C  S  may  be  polarized.  If  the  sur- 
face be  crown-glass  or  water,  the  angle  SCB  must  be  56°  55'  for  the  first, 
and  53°  11'  for  the  second,  in  order  to  give  a  polarized  ray. 

NOTE  206,  p.  180.  A  polarizing  apparatus  is  represented  in  fig.  64, 
where  R  r  is  a  ray  of  light  falling  on  a  piece  of  glass  r  at  an  angle  of  57°, 


Fig.  64. 


the  reflected  ray  r  a  is  then  polarized,  and  may  be  viewed  through  a  piece 
of  tourmaline  in  5,  or  it  may  be  received  on  another  plate  of  glass,  B, 
whose  surface  is  at  right  angles  to  the  surface  of  r.  The  ray  r  s  is  again 
reflected  in  a,  and  comes  to  the  eye  in  the  direction  s  £.  The  plate  of 
mica,  M  I,  or  of  any  substance  that  is  to  be  examined,  is  placed  between 
the  points  r  and  s. 

NOTE  207,  p.  182.  In  order  to  see  these  figures,  the  polarized  ray  r*, 
fig.  64,  must  pass  through  the  optic  axis  of  the  crystal,  which  must  be 
held  as  near  as  possible  to  s  on  one  side,  and  the  eye  placed  as  near 
as  possible  to  s  on  the  other.  Fig.  65  shows  the  image  formed  by  a 
crystal  of  Iceland  spar  which  has  one  optic  axis.  The  colors  in  the 
rings  are  exactly  the  same  with  those  of  Newton's  rings  given  in  Note 
194,  and  the  cross  is  black.  If  the  spar  be  turned  round  its  axis,  the 
rings  suffer  no  change;  but  if  the  tourmaline  through  which  it  is  viewed, 
or  the  plate  of  glass  B,  be  turned  round,  this  figure  will  be  seen  at  the 
angles  0°,  90°,  180°,  and  270°  of  its  revolution.  But  in  the  intermediate 
points,  that  is,  at  the  angles  43°,  135°,  225°,  and  315°,  another  system 
will  appear,  such  as  is  represented  in  fig.  66,  where  all  the  colors  of  the 


Fig.  66. 


430 


JSOTilS. 


The 


rings  are  complementary  to  those  of  fig.  65,  and  the  cross  is  white, 
two  systems  of  rings,  if  superposed,  would  produce  white  light. 

NOTE  908,  p.  182.    Saltpetre,  or  nitre,  crystalizes  in  six-sided  prisms 
having  two  optic  axes  inclined  to  one  another  at  an  angle  of  5°. .  A  slice 


Fig.  67. 


of  this  suhstance  about  the  6th  or  8th  of  an  inch  thick,  cut  perpendicu- 
larly to  the  axis  of  the  prism,  and  placed  very  near  to  s,  fig.  64,  so  that 
the  polarized  ray  rs  may  pass  through  it,  exhibits  the  system  of  rings 
represented  in  fig.  67,  where  the  points  C  and  C  mark  the  position  of  the 
optic  axes.  When  the  plate  B,  fig.  64,  is  turned  round,  the  image 


Fig.  69. 


Fig.lQ. 


NOTE:?.  431 

changes  successively  to  those  given  in  figs.  68,  69,  and  70.  The  colors 
of  the  rings  are  the  same  with  those  of  thin  plates,  but  they  vary  with 
the  thickness  of  the  nitre.  Their  breadth  enlarges  or  diminishes  also 
with  the  color,  when  homogeneous  light  is  used. 

NOTE  209,  p.  183.    Fig.  71  represents  the  ap-  Fig.  71. 

pearance  produced  by  placing  a  slice  of  rock 
crystal  in  the  polarized  ray  rs,  fig.  64.  The 
uniform  color  in  the  interior  of  the  image  de- 
pends upon  the  thickness  of  the  slice ;  but 
whatever  that  color  may  be,  it  will  alternately 
attain  a  maximum  brightness  and  vanish  with 
the  revolution  of  the  glass  B.  it  may  be  ob- 
served, that  the  two  kinds  of  quartz,  or  rock 
crystal,  mentioned  in  the  text,  are  combined  in 
the  amethyst,  which  consists  of  alternate  layers 
of  right-handed  and  left-handed  quartz,  whose 
planes  are  parallel  to  the  axis  of  the  crystal. 

NOTE  210,  p.  187.  Suppose  the  major  axis  A  P  of  an  ellipse,  fig.  18,  to 
be  invariable,  but  the  eccentricity  C  S  continually  to  diminish,  the' 
ellipse  would  bulge  more  and  more  ;  and  when  C  S  vanished,  it  would 
become  a  circle  whose  diameter  is  A  P.  Again,  if  the  eccentricity  were 
continually  to  increase,  the  ellipse  would  be  more  and  more  flattened  till 
CS  was  equal  to  CP,  when  it  would  become  a  straight  line  A  P.  The 
circle  aud  straight  line  are  therefore  the  limits  of  the  ellipse. 

NOTE  211,  p.  187. — The  colored  rings  are  produced  by  the  interference 
of  two  polarized  rays  :.n  different  states  of  undulation,  on  the  principle 
explained  for  common  light. 

NOTE  212,  p.  217. — If  heat  from  a  non-luminous  source  be  polarized  fey 
reflection  or  refraction  at  r,  fig.  64,  the  polarized  ray  r  s  will  be  stopped 
or  transmitted  by  a  plate  of  mica  M I  under  the  same  circumstances  that 
it  would  stop  or  transmit  the  light ;  and  if  heat  were  visible,  images  anal- 
ogous to  those  of  figs.  65,  67,  &c.~would  be  seen  at  the  point  s. 

NOTE  213,  p.  219.— The  Rev.  John  Buchanan,  of  Charleston,  South 
Carolina,  has  recently  shown,  by  ingenious  experiments,  that  the  vulture 
is  directed  to  his  prey  by  the  sense  of  sight  alone. 

NOTE  214,  p.  267. — The  class  Cryptogamia  contains  the  ferns,  mosses, 
funguses,  and  sea-weeds  :  in  all  of  which  the  parts  of  the  flowers  are 
either  little  known  or  too  minute  to  be  evident. 

NOTE  215,  p.  269. — Zoophites  are  the  animals  which  form  madrepores, 
corals,  sponges,  &c. 

NOTE  216,  p.  269.— The  Saurian  tribes  are  creatures  of  the  lizard  or 
crocodile  kind.  Some  of  those  found  in  a  fossil  state  are  of  enormous  size. 

P 

NOTE  217,  p.  315.— When  a  stream  f|,     Fig.  72. 

of  positive  electricity  descends  from  P 
to  n,  fig.  72,  in  a  vertical  wire  at  right 
angles  to  the  plane  of  the  horizontal  ;  * 

circle  A  B,  the  negative  electricity  as- 
cends from  n  to  P,  and  the  force  ex- 
erted by  the  current  makes  the  north 
pole  of  a  magnet  revolve  about  the  •* 
wire  in  the  direction  of  the  arrow- 
heads in  the  circumference,  and  it 
makes  the  south  pole  revolve  in  the 
opposite  direction.  When  the  current 
of  positive  electricity  flows  upward 
from  n  to  P,  these  effects  are  reversed. 


432 


NOTES. 


fig-  73.  w       NOTE  218,  p.  316.— Fig. 

73  represents  a  helix  or 
coil  of  copper  wire,  termi- 
nated by  two  cups  con- 
taining a  little  quicksilver. 
When  the  positive  wire 
of  a  Voltaic  battery  is  im- 
mersed in  the  cup  p,  and 
the  negative  wire  in  the 
cup  n,  the  circuit  is  com- 
pleted. The  quicksilver 
insures  the  connection  between  the  battery  and  the  helix,  by  conveying 
the  electricity  from  the  one  to  the  other.  While  the  electricity  flows 
through  the  helix,  the  magnet  S  N  remains  suspended  within  it,  but  falls 
down  the  moment  it  ceases.  The  magnet  always  turns  its  south  pole  S 
toward  P  the  positive  wire  of  the  battery,  and  its  north  pole  toward  the 
negative  wire. 

NOTE  219,  p.  319. — A  copper  wire  coiled  in  the  form  represented  in  fig. 
73,  is  an  electro-dynamic  cylinder.  When  its  extremities  P  and  n  are 
connected  with  the  positive  and  negative  poles  of  a  Voltaic  battery,  it  be- 
comes a  perfect  magnet  during  the  time  that  a  current  of  electricity  is 
flowing  through  it,  P  and  n  being  its  north  and  south  poles.  There  are 
a  variety  of  forms  of  this  apparatus. 

NOTE  220,  p.  339.— In  fig.  74  the  hyperbola  H  P  Y,  the  parabola  p  P  R, 
and  the  ellipse  A  E  P  L,  have  the  same  focal  distance  S  P,  and  coincide 
through  a  small  space  on  each  side  of  the  perihelion  P  ;  and  aa  a  comet 
is  only  visible  when  near  P,  it  ks  difficult  to  ascertain  which  of  the  three 
curves  it  move*  in.  4 

H 


NOTE  221,  p.  343.— In  fig.  75,  E  A  represents  the  orbit  of  Halley's 
comet,  ET  the  orbit  of  the  earth,  and  S  the  sun.  The  proportions  are 
very  nearly  exact. 


NOTE  222,  p.  360.— Fig.  74  represents  the  curves  in  question.  It  is 
evident  that  for  the  snme  focal  distance  S  P,  there  can  be  but  one  circle 
and  one  parabola  p  PR,  but  that  there  may  be  an  infinity  of  ellipses  be 


NOTES.  433 

tureen  the  circle  and  the  parabola,  and  an  infinity  of  hyperbolas  II  P  Y 
exterior  to  the  parabola  p  P  R. 

NOTE  223,  p.  371  .—Let  A  B,  fig.  26,  be  the  diameter  of  the  earth's  orbit, 
and  suppose  a  star  to  be  seen  in  the  direction  A  S'  from  the  earth  when 
at  A.  Six  months  afterward,  the  earth  having  moved  through  half  of 
its  orbit,  would  arrive  at  B,  and  then  the  star  would  appear  in  the  direc- 
tion B  S',  if  the  diameter  A  B,  as  seen  from  S',  had  any  sensible  magni- 
tude. But  A  B,  which  is  190,000,000  of  miles,  does  not  appear  to  be 
greater  than  the  thickness  of  a  spider's  thread,  as  seen  from  61  Cygni,  sup- 
posed to  be  the  nearest  of  the  fixed  stars. 

NOTE  224,  p.  373. — The  mass  is  found  in  the  manner  explained  in  Note 
133 ;  but  the  method  of  computing  the  distance  of  the  star  may  be  made 
more  clear  by  what  follows.  Though  the  orbit  of  the  satellite  star  is 
really  and  apparently  elliptical,  let  it  be  represented  by  CD  O,  fig.  14,  for 
the  sake  of  illustration,  the  earth  being  in  d.  It  is  clear  that,  when  the 
star  moves  through  C  D  O,  its  light  will  take  longer  in  coming  to  the  earth 
from  O  than  from  C,  by  the  whole  time  it  employs  in  passing^hrough 
O  C,  the  breadth  of  its  orbit.  When  that  time  is  known  by  observation, 
reduced  to  seconds,  and  multiplied  by  190,000,  which  is  the  number  of 
miles  light  darts  through  in  a  second,  the  prod  A  will  be  the  breadth  of 
the  orbit  hi  miles.  From  this  the  dimensions  of  the  ellipse  will  be  ob- 
tained by  the  aid  of  observation,  the  length  and  position  of  any  diameter, 
as  Sp,  may  be  found  ;  and  as  nil  the  angles  of  the  triangle  d  Sp  can  be 
determined  by  observation,  the  distance  of  the  star  from  the  earth  may 
be  computed. 

NOTE  225,  p.  376. — One  of  the  globular  clusters  mentioned  in  the  text 
is  represented  in  fig.  1,  plate  5.  The  stars  are  gradually  condensed  to- 
ward the  center,  where  they  run  together  into  a  blaze  somewhat  like  a 
snowball.  The  more  condensed  part  is  projected  on  a  ground  of  irregu- 
larly-scattered stars,  which  fills  the  whole  field  of  the  telescope.  There 
are  few  stars  in  the  neighborhood  of  this  cluster. 

NOTE  226,  p.  378. — Fig.  2,  plate  5,  represents  one  of  those  enormous 
rings  in  its  oblique  position.  It  has  a  dark  space  in  the  center,  with  a 
small  star  at  each  extremity. 

NOTE  227,  p.  378.— Fig.  3,  plate  5,  may  convey  some  idea  of  the  ring 
in  the  constellation  of  the  Lyre  mentioned  hi  the  text. 

NOTE  228,  p.  378. — This  most  wonderful  object  has  the  appearance  of 
fig.  4,  plate  5.  The  southern  head  is  denser  than  the  northern.  The 
light  of  this  object  is  perfectly  milky.  There  are  one  or  two  stars  in  it. 

NOTE  229,  p.  378. — Fig.  5,  plate  5,  represents  this  brother  system. 

NOTE  230,  p.  379. — Fig.  6,  plate  5,  represents  one  of  the  spindle-shaped 
nebulae. 

NOTE  231,  p.  385.— Elongation.  The  apparent  angular  distance  of  an 
object  from  the  center  of  the  sun. 

28  Oo 


PLATE  I. 


PLATE  II. 


-, 


NEBULAE. 


Page  378. 


PL  5. 


INDEX. 


A. 

ABERRATION  of  light,  30.    Note  98, 

Absorption  of  solar  light  by  the  at- 
mosphere, 15-2. 

of  light  by  colored  media,  155. 

not  inconsistent  with  the  undu- 

latory  theory,  171. 

Acceleration  in  the  mean  motion  of 
the  moon,  36. 

of  Encke's  comet,  346. 

of  Biela's  comet,  347. 

Accidental  colors,  159. 

Achromatic  telescope,  159.  Note  192. 

Action  and  reaction,  5.    Note  19. 

of  light  on  the  retina,  172. 

Adhesion  of  glass  plates,  101. 

Affinity,  chemical,  103. 

Air,  atmospheric,  analysis  of,  111. 

Airy,  Professor,  his  determination  of 
the  inequality  of  the  earth  and 
Venus,  25.  His  experiments  on  the 
motion  of  polarized  light  through 
quartz,  186. 

Algae,  or  sea-weeds,  their  distribu- 
tion, 267. 

Algol,  a  variable  star,  364. 

Alhazen,  the  Saracen,  observed  the 
effects  of  refraction,  150. 

Altitude,  the  height  of  a  celestial 
body  above  the  horizon,  148. 

Ampere,  M.,  his  theory  of  electro- 
dynamics, 319. 

Analogy  between  a  stretched  cord 
and  the  interference  of  light,  188. 

between  the  different  rays  of 

the  solar  spectrum,  220. 

between  light,  heat,  and  sound, 

230. 

Analysis  2.    Note  3. 

Analytical  formulae,  101.    Note  158. 

Analyzing  plate,  a  piece  of  glass,  or 
a  slice  of  a  crystal  used  for  exam- 
ining the  properties  of  polarized 
light,  180. 

Ancient  chronology,  82. 

Angle  of  position  of  a  double  star, 
366. 

Angular  motion  of  the  earth,  86. 
Note  152. 

velocity,  61, 86.    Notes  89, 138, 

152. 

P 


Angular  motions  of  the  first  three  of 
Jupiter's  satellites,  28.  Note  89. 

Animal  electricity,  299. 

Animals,  distribution  of,  269. 

Annual  equation,  34. 

Anomaly,  mean,  37.    Note  106. 

Aphelion,  16.    Note  65. 

Apsides,  9,  16.    Notes  49,  66. 

,  motion  of,  15.    Note  67. 

Arabian  science,  24,  37,  85. 

Arago,  M.,  his  experiments  on  pola- 
rized light,  187,  191.  His  observa- 
tions on  the  temperature  of  the 
earth  and  the  air  above  it,  259.  His 
discovery  of  electricity  from  rota- 
tion, 325.  Hia  Treatise  on  Comets, 
347.  On  the  probability  of  the  earth 
being  struck  by  a  comet,  ib.  He 
proves  that  comets  shine  by  re- 
flected light,  359.  His  estimate  of 
the  number  of  comets,  360. 

Arc  of  the  meridian,  46.  Notes  124, 
125. 

Arcs  a  measure  of  time,  20.  Note  76. 

Areas  proportional  to  the  time,  8. 
Note  41. 

Armature,  a  piece  of  soft  iron  con- 
necting the  poles  of  a  horse-shoe 
magnet,  324. 

Artesian  wells,  243. 

Assyrians  made  use  of  the  week  of 
seven  days,  80. 

Astronomical  tables,  57. 

,  data  for,  57. 

eras,  81.    Note  147. 

Astronomy,  physical,  3. 

-  of  the  Chinese  and  Indians,  83. 

Atmosphere,  analysis,  and  pressure 
of,  112. 

,  the  law  of  its  density,  112. 

-,  the  effect  of  heat  on,  113. 
-,  the  extent  of,  113. 
-,  oscillations  of,  115. 
of  the  moon  and  planets,  238. 

of  the  sun,  238. 

of  comets,  351. 

Atomic  weights,  102. 

Attraction  of  a  sphere  and  spheroid, 

of  the  earth  and  moon,  4. 

of  the  celestial  bodies,  5. 

,  universal,  5. 

P 


446 


INDEX. 


Attraction,  capillary,  109. 

,  electrical,  275. 

,  magnetic,  306. 

of  electric  currents,  319. 

Aurora,  289. 

Axis,  lunar,  64. 

,  major  of  planetary  orbits  inva- 
riable, 19,  71. 

,  connection  of,  with  mean  mo- 
tion, 19. 

Axis  of  rotation,  7,  61.  Notes  34, 137. 

,  principal,  71.    Note  142. 

parallel  to  itself,  61,  74. 

of  the  prism,  173.    Note  199. 

of  a  telescope,  31. 

of  a  cone,  5.    Note  22. 

,  optic,  183.    Note  202. 

of  the  earth's  shadow,  39. 


Babbage,  Mr.,  his  theory  of  volcanic 
action,  249. 

Bacon,  31. 

Back,  Capt.,  cold  suffered  by,  241. 

Bailly,  M.,  on  the  lunar  tables  of  the 
Indians,  83. 

Baily,  Mr.  Francis,  on  the  form  of 
the  earth,  49. 

Barlow,  Mr.,  on  terrestrial  magne- 
tism, 330. 

Barometer,  112. 

Barometrical  measurements,  113. 

Base,  trigonometrical,  46.  Note 
125. 

Batsha,  tides  at,  93. 

Battery,  Voltaic,  291. 

Becquerel,  M.,  his  experiments  and 
opinions  of  electrical  phenomena, 
279.  His  theory  of  atmospheric 
electricity,  281.  His  formation  of 
crystals,  297.  His  thermo-electric 
battery,  328. 

Bessel,  Professor,  his  notice  of  the 
secular  variation  of  the  ecliptie,77. 

Biela,  M.,  discovers  a  comet,  347. 

Binary  systems  of  stars,  365. 

Bissextile,  or  leap-year,  80. 

Biot,  M.,  his  ascent  in  a  balloon,  114. 
His  experiments  on  sound,  131.  On 
circular  polarization,  184.  His 
theory  of  electrical  light,  279.  Of 
terrestrial  magnetism,  330.  On  the 
disturbances  of  terrestrial  mag- 
netism, 332.  His  observations  on 
the  magnetic  force  during  his 
aerostatic  expedition,  334. 

Birds,  their  dispersion,  270. 

Bonnycastle,  Capt.,  his  account  of  a 


luminous  appearance  in  the  s«a, 
288. 

Bonpland,  M.,  his  botanical  obser- 
vations, 266. 

Botto,  Professor,  his  experiments  on 
thermo-electricity,  328,  336. 

Bouguer,  M.,  his  mensuration  of  a 
degree  of  the  meridian  at  the  equa- 
tor, 47. 

Bradley,  Dr.,  his  discovery  of  nuta- 
tion, 76.  His  tables  of  refraction, 
149.  He  mentions  the  two  stars 
of  y  Virginis,  367. 

Brahmins  employed  the  week  of 
seven  days,  80. 

Brewster,  Sir  David,  his  discovery 
of  fluids  in  the  cavities  of  mine- 
rals, 96.  His  analysis  of  solar 
light,  156.  His  law  of  the  polar- 
izing angle,  179.  His  investiga- 
tion of  the  temperature  of  springs, 
252.  His  es  ti  mate  of  the  tern  pera- 
ture  of  the  poles  of  maximum  cold, 
and  of  the  poles  of  rotation,  260.  On 
the  parallelism  of  the  isothermal 
and  geothermal  lines,  ib.  His  ob- 
servations on  phosphorescence, 
286. 

Brinkley,  Bishop,  his  value  of  the 
mass  of  the  moon,  55. 

Brown,  Mr.,  his  botany  of  Australia, 
266. 

Buchan,  Dr.,  his  account  of  a  mi- 
rage, 152. 

Burnes,  Mr.,  his  account  of  a  volca- 
nic elevation,  248. 


C. 

Caesar,  Julius,  his  Calendar,  80. 
Cagniard  de  la  Tour,  M.,  his  inven- 

tion of  the  Syren,  138. 
Callcott,  Mrs.,  her  account  of  the 

earthquake  at  Valparaiso,  248. 
Caloric  the  cause  of  heat,  206. 
-,  the  radiation  of,  207,  220. 
Calorific  rays  of  the  solar  spectrum, 

206. 

-  independent  of  light,  206  et 
seq. 

-  ,  transmission  of  the,  208  et  seq. 

-  ,  reflection  and  absorption  of  the, 
213,  220. 

—  ,  refraction  of,  213. 

—  ,  polarization  of,  215. 
Calotype,  194. 
Capillary  attraction,  108. 

-  of  tubes,  108.    Notes  168,  169, 
170. 


INDEX. 


447 


Capillary  attraction  of  plates,  111  et 

seq.    Notes  171,  172. 
Center  of  gravity,  4.    Note  10. 
of  the  solar  system,  its  motion, 

7,23.    Note  82. 

of  the  universe,  23. 

Centrifugal  force,  5,  94.    Notes  18, 

Chaldeans,  their  observations  of 
eclipses,  35,  37. 

Chemical  rays  of  the  solar  spec- 
trum, 207. 

,  transmission  of,  207. 

Chemical  affinity,  103. 

Chinese  science,  83,  85. 

Chladni,  his  experiments  on  vibra- 
ting plates,  140.  Note  179. 

Christian  era,  80. 

Chromatype,  196. 

Clairaut,  his  computation  of  the  dis- 
turbances of  Halley's  comet,  342. 

Cleavage,  107. 

Climate,  253. 

,  stability  of,  262. 

of  the  planets,  238. 

Climates,  excessive,  261. 

Coal  measures,  their  early  forma- 
tion, 70. 

Cobalt,  a  metal,  its  polarity,  305. 

Cohesion,  96  et  seq. 

Cohesive  force,  the  intensity  of,  104. 

Cold  at  Melville  Island,  241. 

Colladon,  M.,  his  experiments  on 
sound  under  water,  129. 

Collision  of  a  comet,  72,  347. 

Colored  media,  their  action  on  light, 
]55,  169. 

fringes,  162,  168  et  geq. 

Colors,  prismatic,  154  et  seq. 

,  accidental,  159. 

,  complementary,  160. 

of  the  stars,  374. 

Columbus  discovers  the  variation  of 
the  compass,  305.  His  account  of 
the  Gulf-weed,  267. 

Coma  Berenices,  the  constellation, 
nebula*  in  it,  374. 

Comet,  Halley's,  341. 

,  Lexel's,  340. 

,  Encke's,  345. 

,  acceleration  of  a,  345. 

,  Biela  or  Gambart's,  347. 

,  shock  of  a,  348. 

of  the  year  1680,  348. 

Comets,  337. 

,  orbits  of,  339,  350. 

• —  ,  fall  of,  to  the  sun,  350 

,  masses  of,  352. 

,  tails  of,  354. 


Comets,  nebulosity  of,  352,  356. 

,  light  of,  aV7. 

,  number  of,  360. 

Compass.    See  Mariner's 
Compress-ion,  4.    Note  11. 

of  a  spheroid,  6. 

of  the  terrestrial  spheroid,  38, 

48,49.    Note  31. 

of  Jupiter,  7,  61. 

of  a  fluid  mass  in  rotation,  38. 

Concentric  hollow  sphere,  its  attrac 

tion,  4.    Note  8. 

elliptical  strata,  44.    Note  120. 

Cone,  5.    Note  22. 

Configuration  or  relative  position  of 

Jupiter  and  Saturn,  24.    Note  85. 
,  of  Jupiter's  satellites,  27.  Note 

88. 

of  land  and  water,  258. 

Conic  sections,  5.    Note  22. 

Conjunction,  24.    Note  83. 

,  contemporaneous,  of  planets, 

41. 
Connection  between  the  variations 

of  the  eccentricity  and  apsides, 

Connection  between  the  variations 

of  the  nodes  and  inclination,  19. 

Note  75. 

Convexity  of  the  earth,  50. 
Coordinates  of  a  planet,  10.    Note 

56. 
Cosine  and  sine  of  an  arc,  20.  Note 

76. 

of  latitude,  45.    Note  123. 

Cook,  Capt.,  the  object  of  his  first 

voyage,  52. 
Cordier,  M.,  on  the  heat  of  the  earth, 

242. 
Coulomb,   his  balance    of  torsion, 

27*. 
Gumming,    Professor,    his    experi 

merits   on  thermo-electricity  and 

magnetic  currents,  328. 
Cryptogamia,  267.    Note  214. 
Crystalization,  105. 

,  the  water  of,  106. 

— • ,  effects  of  heat  on,  106. 

Cube,  107.    Note  163. 

Cubes  of  mean  distances,  5.    Noly 

26. 

Currents  in  the  ocean,  94. 
of  electricity,  287  et  aeq.,  314 

et  aeq. 
Curves  of  the  second  order,  or  conic 

sections,  5.    Note  22. 
of  double  curvature  are  lines 

curved  in  two  directions,  like  a 

cork-screw  or  helix,  183. 


448 


Cyanotype,  197. 

Cylinder  or  tube,  vibration  of,  147. 

,  electro-dynamic,  319.     Note 

219. 


Daguerreotype,  195 

Dalton,  Dr.,  his  laws  of  definite  pro- 
portion, 102.  His  experiments  on 
evaporation,  228. 

Damoiseau,  M.,  his  computation  of 
the  perturbations  of  Biela's  comet, 
347. 

Daubuisson,  M.,  on  the  temperature 
of  mines,  242. 

Davy,  Sir  Humphry,  his  opinion  of 
electric  light,  279.  His  decompo- 
sition of  the  earths  and  alkalies, 
296.  His  experiments"  on  the  trans- 
mission of  the  electric  fluid,  335. 

Davy,  Dr.,  his  experiments  on  ani- 
mal electricity,  335. 

Day,  the  length  of,  invariable,  72. 

,  astronomical  and  sidereal,  81. 

Note  145. 

Declination,  83,  89.    Note  154. 

,  cosine  of,  90.    Note  154. 

Definite  proportion,  102. 

of  electricity,  103. 

Degrees,  minutes,  and  seconds  of 
arcs,  9.  Note  50. 

of  the  meridian,  mensuration 

of,  46. 

Delambre,  M.,  his  computations 
show  that  the  length  of  the  year 
has  not  been  increased  by  the 
action  of  comets,  338. 

De  la  Rive,  M.,  determines  the  tem- 
perature of  an  Artesian  well,  244. 

De  Laroche,  M.,  his  experiments  on 
the  transmission  of  caloric,  210. 

Density  of  bodies,  56. 

of  the  sun  and  planets,  56. 

of  the  ocean,  45,  48. 

of  the  earth,  73. 

Depth  of  the  ocean,  50,  72,  86. 

Deviation  of  light.    Note  191. 

Dew,  the  formation  of,  221. 

Diameter,  2.    Note  1. 

of  the  sun  and  earth,  55. 

of  the  moon,  Jupiter,  and  Pal- 
las, 26,  51,  55. 

,  apparent,  of  the  sun  and  plan- 
ets, 38,  55.  Note  110. 

Dicotyledonous  plants,  267. 

Diffraction  of  light,  168,  175.  Notes 
193,  196,  197. 

Dip,  magnetic,  301. 


Disc,  the  apparent  surface  of  a  heav- 

enly body,  29. 
Dispersion  of  light,  158.    Note  90. 

-  on  the  undulatory  theory,  191. 
Displacement  of  Jupiter's  orbit  and 

equator,  28.    Note  90. 
Distance  of  the  sun  and  planets,  53. 
Note  132. 

-  of  the  moon,  4,  33.    Note  17. 

-  ,  perihelion,  10.    Note  57. 

-  of  the  fixed  stars,  54,  362. 

-  may  ie  found  from  the  multi- 
ple systems,  370. 

-  ,  lunar,  37. 

-  ,  inverse  square  of  the,  5.    Note 
23. 

-  ,  zenith,  83.    Note  149. 
Disturbing  force,  14.    Note  63. 

-  of  the  sun,  34,  78.    Note  101. 

-  of  the  planets  on  the  moon,  35. 

-  of  the  moon  on  the  earth,  74. 

-  of  the  moon  on  herself,  35. 
Division  of  time,  78. 

-  ,  decimal,  79. 

Doabereiner,  M.,  his  experiments  on 
the  combustion  of  platina,  104. 

Dollond,  Mr.,  his  achromatic  tele- 
scope, 159. 

Double  refraction,  175.    Note  200. 

-  stars,  365. 

Dunlop,  Mr.,  his  catalogue  of  double 

stars,  368. 
Duperrey,  Captain,  his  determina 

tion  of  the  magnetic  equator,  302. 
Dusejour,  M.,  proves  that  a  comet 

cannot  remain  long  near  the  earth, 

338. 
Dynamics,  the  science  of  force  and 

motion,  308. 


Earth,  form  of  the,  5,  43. 

-  ,  from  arcs,  45. 

-  ,  from  pendulum,  47. 

-  ,  from  lunar  theory,  39. 

-  ,  from  precession  and  nutation, 
50. 

-  ,  from  the  mean  of  all,  49. 

-  ,  mean  diameter,  circumference, 
polar  and  equatorial  radius  of  the, 

-  ,  density  of  the,  56,  73. 

-  ,  internal  structure  of  the,  73. 

-  ,  central  heat,  and  temperature 
of  the,  67  et  seq.,  241  et  seq. 

-  ,  magnetism  of  the,  300. 

-  ,  magnetic  by  induction,  330. 

-  ,  rotation  of  the.    See  Rotation, 


INDEX. 


449 


Earthquakes,  248. 

• ,  noise  of,  132. 

Echoes,  13-2. 

Eclipses  of  the  sun,  40.    Note  1 14. 

of  the  moon,  39.     Xote  109. 

of  Jupiter's  satellites,  29.  Notes 

93,  94. 

of  the  planets,  41. 

Ecliptic,  8. 

,  plane  of,  10. 

,  secular  variation  of,  19, 75,  77. , 

Egyptians,  their  year  and  week,'  80.  j 
Elastic  bodies,  vibrations  of,  135  et 

seq.     See  Vibration. 
Elasticity  of  the  atmosphere,  112  et  \ 

of  matter,  96. 

Electric  induction,  276. 

intensity,  277  et  seq. 

tension,  278. 

clouds,  281. 

currents,  291,  314,  319  et  seq. 

and  magnetic  currents,  319  et 

seq. 

machines,  333. 

Electricity,  common,  271. 

,  effects  of,  282,  £86. 

,  sources  of,  271,  280. 

,  atmospheric.  281. 

,  velocity  of,  284. 

,  Voltaic,  290  et  seq. 

,  animal,  299. 

,  thermal,  328. 

by  rotation,  325. 

producing  rotation,  316. 

of  metallic  veins,  332. 

,  magneto,  322. 

,  identical  with  magnetism,  325.  ; 

,  identity  of  all  the  kinds,  336.    j 

Electrics  and  non-electrics,  271   et  ] 

seq. 

Electro-magnetism,  314. 
magnetic  induction,  317,  318. 

•  magnets,  317. 

dynamic  cylinders,  319.    Xote 

219. 

dynamics,  319. 

Elements  of  the  planetary  orbits,  9. 
Note  57. 

,  how  founded  from  observa- 
tion, 58.    Note  135. 

Elements  of  parabolic  orbits,  339. 

of  stellar  orbits,  364. 

Ellipse,  a  conic  section,  5.    Note  24. 

,  the  limits  of,  187.    Note  210. 

Ellipsoid,    oblate    and    prolate,    4. 
Note  9. 

of  revolution,  44.    Note  119. 

,  terrestrial.  49. 

29 


Elliptical  or  true  motion,  8.  Note 
39. 

Encke,  Professor,  his  determination 
of  the  orbit  and  motion  of  the 
comet  named  after  him,  346.  Of 
its  acceleration,  346.  And  of  the 
orbit  of  the  star  70  Ophiuchi,  367. 

Epoch,  the,  10. 

,  longitude  of  the,  10. 

Equation  of  the  centre,  9,  34.  Note 
48. 

of  time,  78. 

Equator,  4.    Note  11. 

Equilibrium,  stable  and  unstable,  12. 
Note  60. 

Equinoctial,  9.    Note  46. 

Equinoxes,  9.    Note  46. 

Era,  the  Christian,  80. 

Eratosthenes  'measures  a  degree  of 
the  meridian  between  Syene  and 
Alexandria,  48. 

Ether,  its  nature,  171. 

Ethereal  medium,  21,  97,  171. 

,  temperature  of,  239. 

,  resistance  of,  337. 

,  vibrations  of,  171,  193,  194. 

,  elasticity  of,  31.    Note  99. . 

Eudoxiis  describes  the  state  of  the 
heavens  about  the  time  of  the 
Trojan  war,  84. 

Evection,  a  lunar  inequality,  34. 
Note  103. 

Eccentricity,  9.    Note  52. 

,  secular  variation  of  the,  17. 

of  the  orbits  of  Jupiter's  satel- 
lites, 27. 

of  lunar  orbit  constant,  36. 

of  the  terrestrial  orbit  diminish- 
ing, 19. 

of  the  terrestrial  orbit,  its  varia- 
tion the  cause  of  the  acceleration 
in  the  moon's  mean  motion,  37. 

Expansion  of  substances  by  heat, 
222. 

Extraordinary  refraction,  150. 

ray  and  image,  173. 

F. 

Fall  of  heavy  bodies,  6,  49. 

at  the  surface  of  the  sun  and 

planets,  56. 

Fall  of  meteorites,  381. 

Faraday,  Dr.,  reduces  the  gases  to  a 
liquid  state.  99.  His  causes  of 
affinity,  103.  His  experiments  on 
spontaneous  combustion,  ib.  His 
theory  of  the  aurora,  289.  His 
views  nf  electro-chemical  decom- 


450 


INDEX. 


position,  297.  His  experiments 
on  the  transmission  of  electricity, 
299.  He  produces  rotatory  motion 
by  the  electric  force,  315.  His 
experiments  on  magneto-electri- 
city, 322.  He  proves  the  identity 
of  the  electric  and  magnetic  fluids, 
324.  His  explanation  of  electrici- 
ty evolved  by  rotation,  325.  His 
classification  of  magnetic  sub- 
stances, 327.  His  experiments  on 
the  induction  of  terrestrial  mag- 
netism, 332.  He  supposes  rota- 
tion a  cause  of  electric  currents 
in  the  earth,  333.  On  the  evolu- 
tion of  electric  currents,  and  iden- 
tity of  the  different  kinds  of  elec- 
tricity, 336. 

Faye's  comet,  341. 

Fiedler,  Dr.,  his  fulgorites,  283. 

Figure  of  the  earth.     See  Earth. 

Fluids,  the  undulations  of,  93.  Note 
156. 

,  compression  of,  99. 

,  capillary  attraction  of,  111. 

Focal  distance,  5.    Note  22. 

length  of  a  lens.    Note  196. 

Foei  of  an  ellipse,  5.    Note  22, 

Forbes,  Professor,  his  experiments 
on  heat,  polarization  of,  216.  On 
the  heat  of  moonlight,  239.  His 
experiments  during  the  annular 
eclipse  of  the  sun,  158. 

Force,  the  unknown  cause  of  mo- 
tion, 4  ct  passim. 

proportional  to  velocity,  8.  Note 

,  gravitating,  6.  See  Gravita- 
tion. 

,  centrifugal,  5,  43.  Notes  18, 

117. 

,  molecular,  96. 

,  electric,  274. 

of  lightning,  282. 

Forces  which  fix  the  nature  of  the 
conic  sections  in  which  the  plan- 
ets and  cornets  move;  360.  Note 
222. 

Foster,  Capt.,  remarks  on  the  clear- 
ness with  which  sound  is  trans- 
mitted over  ice,  130. 

Fourier,  M.,  his  estimate  of  the  tem- 
perature of  space,  240.  On  the 
decrease  of  central  heat,  245. 

Fox,  Mr.,  on  the  temperature  of 
mines,  242.  On  the  law  of  mag- 
netic intensity,  308.  On  currents 
of  electricity  in  metallic  veins,  331. 

Franklin,  Sir  John,  his  observations 


on  the  temperature  of  the  Arctic 
regions',  260. 

Fraunhofer,  Professor,  his  dark  lines 
in  the  solar  spectrum,  157.  His 
solar  spectrum,  193. 

Fresnel,  M.,  proves  the  extfaordina 
ry  ray  to  be  wanting  in  some  sub- 
stances, 177.  His  experiments  on 
circular  and  elliptical  polari/a 
tion,  186;  and  on  light  passing 
through  the  axis  of  quartz,  187. 
On  the  interference  of  light,  188. 

Fringes  of  color  about  circular  aper 
tures,  168.  Note  196. 

Fulgorites,  283. 

Fundamental  note  in  music,  335. 

G. 

Galileo  first  observed  the  nodal 
points  of  vibrating  bodies,  140. 

Galvani,  Professor,  his  discoverv 
290. 

Galvanometer,  318. 

Gambart,  M.,  his  computation  of 
the  elements  of  a  comet,  347. 

Gardner,  Mr.,  on  the  configuration 
of  land  and  water,  258. 

Gay-Lussac,  M.,  his  law  of  the  com- 
bination of  gases,  103.  His  esti- 
mation of  the  length  of  a  flash  of 
lightning,  282. 

Gensannc,  M.,  his  observations  on 
the  heat  of  mines,  242. 

Giesecke,  Sir  Charles,  on  isothermal 
lines,  260. 

Glass  impermeable  to  heat,  210  et 
scq. 

prism,  153.    Note  190. 

,  crown  and  flint,  properties  of, 

J58. 

— ,  polarizing  angle  of,  179.  Note 
205. 

,  vibrations  of,  141. 

Goodricke,  M.,  his  opinion  of  varia- 
ble stars,  365. 

Graham,  his  compensation  pendu- 
lum, 224. 

Gravitation,  3,  44.    Note  5. 

,  terrestrial.  4. 

— -decreases  from  the  poles  to  the 
equator,  44. 

,  the  intensity  of,  4.    Note  13. 

of  the  planets  and  satellites,  5. 

Note  28. 

,  universal,  6  et  scg. 

,  the  nature  of,  386. 

proportional  to  the  mass,  5. 

Notes  27,  28: 


INDEX. 


451 


Gravitation,  a  consequence  of  elec 
trie  action,  97  et  seq. 

Gravity,  the  direction  of,  43. 

Great  inequality  of  Jupiter  and  Sat- 
urn, 24,  83. 

Great  comet  of  1843,  350. 

Grimaldi,  his  discovery  of  colored 
fringes  on  the  borders  of  shadows, 
169. 

Grylli,  grasshoppers,  crickets,  lo- 
custs, &c.,  125,  126. 

Gymnotus  elect ricus,  299. 

H. 

Haidinger.  M.,  his  experiments  on 
crystalization,  105. 

Hall,  the  first  to  construct  an  achro- 
matic telescope,  159. 

Bailey's  comet,  341. 

Hanstein,  Professor,  discovers  all 
substances  to  be  magnetic  in  a 
certain  position,  305. 

Harmonic  divisions  of  a  musical 
string,  134. 

divisions  of  a  column  of  air, 

137. 

Harmony,  136. 

Harris,  Mr.  Snow,  his  experiments 
oa  electricity,  276  et  seq. 

Harrison,  Mr.,  his  compensation  pen- 
dulum, 224. 

Hearing,  the  extent  of,  126. 

,  experiments  of  Dr.  Wollaston 

on,  125. 

• ,  experiments  of  M.  Savart  on, 

126. 

Heat,  theory  of,  206. 

,  transmission  of,  208. 

of  various  kinds,  210. 

,  solar,  trcnsmission  of,  213. 

,  maximum  point  of,  in  solar 

spectrum,  214. 

,  polarization  of,  215. 

,  analogy  between  light  and, 

218. 

,  radiant,  220. 

,  expansion  by,  222. 

,  propagation  of,  225. 

,  latent,  227. 

,  application  of,  229. 

,  supposed  to  consist  of  undu- 
lations of  the  ethereal  medium, 
230. 

,  solar,  231  et  seq. 

,  quantity  of  solar,  252. 

,  quantity  of  solar  lost  and  gain- 
ed by  the  earth,  invariable,  261. 

,  central,  of  earth,  241  et  seq. 


Heat,  superficial,  of  earth,  252. 

,  distribution  of,  253. 

,  influence  of,  on  vegetation, 

262. 

Height  of  atmosphere,  114. 

of  tides,  91. 

of  mountains,  7. 

Heliacal  rising,  80.    Note  146. 

Helix,  circular  and  elliptical,  186. 

Henry,  Professor,  his  temporary 
magnet,  317. 

Herschel,  Sir  William,  his  discov- 
ery of  the  satellites  of  Saturn  and 
Uranus,  32 ;  of  the  rotation  of  Ju- 
piter's satellites,  65  ;  of  the  calo- 
rific rays  of  the  solar  spectrum, 
199.  His  observations  on  the  point 
of  maximum  heat  in  the  solar 
spectrum,  .214.  His  account  of 
the  nucleus  of  the  comet  of  1811, 
352.  Number  of  fixed  stars  he 
saw  in  one  hour,  361.  His  cata- 
logue of  double  stars,  and  discov- 
ery of  the.  binary  systems,  365. 
His  observations  of  TT  Serpentarii, 
and  of  g  Orionis,  368.  On  the 
motion  of  the  solar  system,  370. 
His  observations  on  the  Milky 
Way,  374.  On  clusters  of  stars, 
375.  On  the  nebulae,  376.  His  si- 
dereal astronomy,  381. 

Herschel,  Sir  John,  his  estimation 
of  the  thickness  of  Jupiter's  ring, 
62.  He  ascribes  the  decrease  of 
the  earth's  temperature  to  the  se- 
cular variation  of  the  eccentricity 
of  the  earth's  orbit,  70.  On  the 
decrease  of  heat  in  the  northern 
hemisphere,  ib.  Proposes  the  use 
of  equinoctial  time,  81.  His  re- 
marks on  the  clearness  of  sound 
during  the  night,  130.  On  thun- 
der, 132.  His  discovery  of  two 
new  prismatic  colors,  156.  His 
argument  in  favor  of  the  undula- 
tory  theory  of  light,  169.  On  the 
phenomena  of  polarization  of 
light,  172.  On  polarizing  appa- 
ratus, 183.  His  discoveries  in  the 
photographic  spectrum,  197.  On 
the  discontinuity  of  calorific  spec- 
trum, 206.  His  discovery  of  the 
parathermic  rays,  231.  His  theory 
of  volcanic  action,  249.  Supposes 
the  ether  may  be  in  motion,  350. 
On  the  contraction  of  the  heads 
of  comets,  356.  On  the  gravita- 
tion of  the  binary  systems,  362. 
His  estimation  of  the  distances  of 


452 


the  fixed  stars,  ib.  He  misses  a 
star,  363.  His  account  of  the  star 
Algol,  364.  Determines  the  ellip- 
tical motions  of  binary  systems, 
367.  Determines  the  orbit  of  y 
Virginis,  ib.  Adds  to  the  cata- 
logue of  double  stars,  368.  On 
the  color  of  the  stars,  374.  On 
clusters  of  stars,  ib.  On  the  ne- 
bula;, 376  et  seq. 

Herschel,  Miss  Caroline,  her  obser- 
vations of  Encke's  comet,  345. 
Her  catalogue  of  nebulae,  376. 

Hevelius  first  noticed  the  contrac- 
tion of  comets  in  approaching  the 
eun,  356.  Thought  he  saw  the 
phasesof  a  comet,  357.  Mentions 
a  variable  star,  364.  His  obser- 
vations of  Halley's  comet,  343. 

Hipparchus  discovers  precession,  75. 
His  catalogue  of  stars,  363. 

Homogeneous  light,  154. 

• spheroid,  its  rotation,  44. 

Horizontal  refraction,  39.    Note  113. 

- —  parallax  of  the  moon,  51. 

Horoscope,  84. 

Hit m bold t,  Baron,  his  observations 
on  the  Gulf-stream,  04.  Effects 
.of  the  rarity  of  the  air  on,  114. 
His  observations  on  the  transmis- 
sion of  sound,  189.  On  the  tem- 
perature of  mines,  242.  On  the 
distribution  of  heat,  254.  His  bo- 
tanical observations,  266.  On  the 
distribution  of  plants,  267.  On 
the  Gulf-weed,  268.  His  observa- 
tions on  terrestrial  magnetism, 
330. 

Hurricanes,  laws  of,  119. 

Huygens,  his  undulatory  theory  of 
light,  163. 

Hyperbola,  12.    Note  22. 

I. 

Ibn  Junis,  his  observations,  85. 

Ice,  its  double  refraction,  177. 

useful  for  polarizing  light,  183. 

—  impermeable  by  Voltaic  elec- 
tricity, 298. 

Icebergs  drifted  from  the  poles,  95. 

collision  of,  a  cause  of  light, 

280. 

Iceland  spar,  a  carbonate  of  lime, 
its  form,  175.  Note  166. 

— — ,  a  doubly  refracting  substance, 
176.  Note  200. 

— —  useful  as  an  analyzing  plate, 
181 


Iceland  spar  a  negative  crystal,  177. 

Image  from  a  crystal  with  one  op- 
tic axis,  183.  Note  207. 

from  a  crystal  with  two  optic 

axes,  182.     Note  208. 

Impetus,  a  force  proportional  to  the 
mass  and  the  square  of  the  ve- 
locity of  the  striking  body  con- 
jointly, 131. 

Imponderable  agents,  336. 

Inactive  lines  in  photographic  spec- 
trum, 204. 

Inclination  of  planetary  orbits,  9. 
Note  53. 

variation  of,  18.     Note  72. 

Indians,  the  lunar  tables  of,  83. 

Inequalities.    See  Perturbations. 

Insects,  the  distribution  of,  270. 

Intensity  of  light,  164. 

of  sound,  124,  130. 

of  gravitation,  4. 

Interference  of  waves,  92.  Note  147. 

of  tides  at  Batsha  in  Tonquin, 

93. 

of  sound, 133. 

of  light,  161,  187.    Notes  193, 

211. 

Internal  heat  of  the  earth,  67,  242 
et  seq. 

structure  of  the  earth,  74. 

structure  of  Jupiter,  28,  57. 

structure  of  Saturn  and  Mars, 

57. 

Invariable  plane  of  the  solar  system, 
22.     Note  80. 
— ,  position  of,  22.    Note  81. 

of  the  universe,  23. 

i  Inverse  square  of  distance,  5.     Note 
I      23. 

cube  of  distance,  55.    Note  ]  33. 

Iron,  its  magnetic  properties,  305, 
327. 

Isogeothermal  lines,  260. 

Isomorphism,  106. 

Isothermal  lines,  259. 

Ivory,  Mr.,  his  determination  of  the 
form  of  the  terrestrial  spheroid, 
43,  47.  His  formuhe  for  baro- 
metrical measurements,  113.  On 
the  distribution  of  the  electric  flu- 
id, 276. 


Jews  used  the  week  of  seven  days, 

80. 

Jovial  System,  the  mass  of,  55. 
Julian  Calendar,  80. 
Jupiter,  the  compression  of,  62. 


453 


Jupiter,  magnitude  of,  56. 

,  mass  of,  55. 

,  rotation  of,  61. 

,  precession  and  nutation  of,  28. 

,  in  conjunction  and  opposition, 

30.    Note  96. 
and  Saturn,  their  theory,  24. 

Note  84. 
Jupiter's  satellites,  theory  of,  26. 

,  masses  of,  26,  54. 

,  orbits*  of,  26,  27.    Notes  86, 87. 

,  law  in  the  mean  motions  and 

mean  longitudes  of,  28. 
,  svnodic  motions  of,  29.    Note 

92. 

,  eclipses  of,  29.    Notes  93,  94. 

,  configuration  of,  27.    Note  88. 

,  effect  of  Jupiter's  form  on,  26. 

,  secular  variations  of,  27  et  seg. 

,  periodic  variations  of,  28. 

,  effects  of  the  displacement  of 

Jupiter's  equator  and  orbit  on,  28. 

Note  90. 

,  rotation  of,  65. 

,  libration  of,  64. 


Kaler.  Capt.,  determines  the  length 
of  the  seconds  pendulum  at  Lon- 
don, 84. 

Kempelen  and  Kratzenstein,  their 
speaking  machine,  147. 

Kepler  discovers  the  form  of  the 
planetary  orbits,  5.  Note  26.  His 
laws,  ib. 

Kupffer,  M.,  his  observations  on  the 
isothermal  lines,  and  the  poles  of 
maximum  cold,  261.  Discovers 
a  nocturnal  variation  in  the  com- 
l«ss,  303. 


La  Grange,  M.,  proves  the  stability 

of  the  Solar  System,  22. 
Lalande,  M.,  his  computation  of  the 

contemporaneous  conjunctions  of 

the  planets,  41. 
Laminae,  vibrations  of,  140.    Notes 

181,  lr-J. 
Lamouroui,  M.,  on  the  distribution 

of  sea-weeds,  267. 
Languages,  collation  of,  270. 
,  vocal  articulation  of,  imitated 

by  machines,  147. 

La  Place,  the  Marquis,  his  determi- 
nation of  the  invariable  plane,  22 ; 

and  of  the  great  inequality  of  Ju 


piter  and  Saturn,  24.  Proves  that 
the  lunar  perigee  and  nodes  are 
not  affected  by  the  resistance 
of  ether,  36.  He  discovers  the 
cause  of  the  lunar  acceleration, 
ib.  His  theory  of  spheroids,  43. 
He  ascribes  the  motions  of  the 
planets  to  a  common  original 
cause,  61 .  Proposes  the  year  1250 
as  a  universal  epoch,  81.  Quota- 
tion from,  82.  Proves  the  Indian 
tables  to  be  as  recent  as  Ptolemy, 
83.  Proves  that  the  discrepancy 
between  Newton's  theory  of  the 
tides,  and  observation,  depends 
upon  the  depth  of  the  sea,  86.  On 
the  utility  of  investigations  of 
cause  and  effect,  90.  On  capilla- 
ry attraction,  109.  On  the  oscil- 
lations of  the  atmosphere,  115. 
On  the  comet  of  1770,  338.  On 
Halley's  comet,  342.  On  the  ex- 
tent of  solar  attraction,  344.  On 
the  comet  of  1682,  357.  On  the 
origin  of  the  Solar  System,  377. 

Latent  heat,  226. 

Latitude,  terrestrial,  4.    Note  11. 

,  celestial,  9.    Note  54. 

,  square  of  the  sine  of  the,  47. 

Note  126. 

Length  of  a  wave,  124. 

of  the  seasons  variable,  69. 

of  the  day  invariable,  66. 

of  the  civil  year,  79. 

of  the  Egyptian  year,  80. 

of  a  degree  of  the  meridian, 

46. 

of  the  pendulum  at  London, 

84. 

of  the  tails  of  comets,  355. 

Lens,  159.  The  glasses  of  a  tele- 
scope and  of  spectacles  are  lenses. 

Leslie,  Sir  John,  his  theory  of  the 
internal  structure  of  the  globe,  73. 
On  radiant  heat,  207. 

Level  of  the  sea,  84.    Note  150. 

Lexel,  M.,  his  comet,  340. 

Libration  of  the  moon,  64. 

of  Jupiter's  satellites,  64. 

Light,  148. 

,  velocity  of,  31. 

,  reflection  and  refraction  of, 

148,  170.  Notes  184,  198. 

,  analysis  of,  154.    Note  190. 

,  absorption  of,  154. 

,  intensity  of,  164. 

,  dispersion  and  deviation  of, 

158,  191. 

,  propagation  of,  164,  171. 


454 


Light,  interference  of,  161,  187. 

,  diffraction  of.  168.    Notes  193, 

196,  197. 

of  sun  and  moon,  239. 

of  comets,  357. 

of  fixed  stars,  362. 

action  of,  on  retina,  172. 

electric,  279. 

l>olarizalion  of,  173. 

emanating  theory  of,  161. 

undulatory  theory  of,  162  etseq. 

objections  to  the   undulatory 

theory  of,  removed,  190. 

,  length  and  frequency  of  the 

undulations  of,  161. 

Lightning  and  its  effects,  282. 

,  its  velocity,  284. 

Lines  of  the  second  order,  or  conic 
sections,  5.  Note  22. 

of  no  variation,  301. 

of  perpetual  snow,  256. 

,  isothermal,  259. 

,  isogeothermal,  252. 

Longitude,  terrestrial,  6,  30,  41. 
Notes  11,  95. 

,  celestial,  9.    Note  47. 

of  perihelion,  10. 

of  nodes,  10. 

of  epoch,  10. 

Lunar  theory,  33. 

inequalities,  34. 

eclipses,  39. 

distance,  42. 

spheroid,  64. 

Lunar  orbit,  33. 

—• — ,  eccentricity  and  inclination  of, 
constant,  35. 

,  nutation  of,  39. 

Lyell,  Mr.,  on  the  temperature  of  the 
northern  hemisphere,  70.  His  es- 
timate of  the  number  of  volcanic 
eruptions,  246. 

M. 

Mackintosh,  Sir  James,  a  quotation 
from  his  "General  View  of  the  Pro- 
gress of  Ethical  Philosophy,"  1; 

Magnets,  305.  ' 

,  temporary,  317  et  seq. 

Magnetic  meridian,  301. 

polarity  of  the  earth,  301. 

dip  and  equator,  301. 

poles,  300. 

intensity  of  the  earth,  302. 

induction,  306. 

force,  308. 

fluid,  308. 

and  electric  forces,  310. 


Magnetism  in  general,  305. 

of  different  substances,  305. 

and  electricity  identical,  3-23. 

of  the  sun  and  planets,  334. 

,  terrestrial,  300,  330. 

Magneto-electricity,  322. 

Major  axis  of  an  ellipse.     Note  23. 

of  an  orbit,  8.    Note  42. 

,  secular  motion  of,  17. 

of  planetary  orbits  invariable 

in  length,  19. 

Malus,  M.,  his  discovery  of  the  po- 
larization of  light,  189. 

Mankind  identical  in  species,  270. 

Marcet,  M.,  on  the  tempuralure  of 
an  Artesian  well,  244. 

Marco  Polo  finds  a  difficulty  of  kin- 
dling fire  at  great  heighls,  114. 

Marine  plants,  their  distribution, 
267. 

Mariner's  compass,  304. 

,  variation  of,  301. 

Mars  eclipsed  Jupiter,  41 

,  parallax  of,  53. 

,  compression  of,  57. 

,  climate  of,  239. 

Mass,  6.    Note  27. 

of  the  sun  and  planets,  55. 

of  Jupiter's  satellites,  55. 

of  the  moon,  55. 

of  Jupiter  and  the  Jovial  sys- 
tem, 55. 

of  comets,  352. 

Mathematical  and  Mechanical  Sci- 
ences, 2.  Note  2. 

Matter,  proportion  of,  in  any  two 
planets,  55.  Note  133. 

,  the  ultimate  particles  of,  96  et 

seq. 

,  the  attraction  of,  4.    Note  5. 

,  its  diffusion  in  space,  381. 

Maximum  squares,  59.     Note  136. 

point  of  heat  in  solar  spectrum, 

214. 

Mayer,  M.,  his  catalogue  of  stars, 
367. 

Mean  time,  78. 

distance,  8.     Note  41. 

motion,  9.     Notes  43,  45. 

longitude,  9.     Note  47. 

motions  and  major  axes,  their 

constancy,  19. 

motions  of  Jupiter  and  Saturn, 

law  of,  24. 

motions  of  Venus  and  the  earth, 

25. 

motions  of  Jupiler's  satellites, 

law  of,  27. 

Measures,  standard?  of,  84. 


KNDEX. 


455 


Melloni.  M..  his  experiments  on  the 
transmission  of  caloric,  208  et  seq. 

On  the  point  of  maximum  heat  on 
the  solar  spectrum,  215. 

Mercurv,  the  planet,  rotation  of,  60. 

— -,  cl'imate  of,  240. 

Meridian,  46. 

,  mensuration  of,  46.    Note  124. 

,  form  of,  47. 

,  quadrant  of,  83. 

Messier,  M.,  on  Lexers  comet,  340. 
Was  the  first  who  observed 
Encke's  comet,  345. 

Metals,  dilatation  of,  223. 

Meteorites,  381. 

Meteors  and  shooting  stars,  382. 

Metre,  a  French  measure,  84. 

Mica,  its  action  on  light,  180,  181. 

Milky  Way,  54,  374. 

Mines,  temperature  of,  242. 

Minor  axis  of  an  ellipse,  5.    Note  24. 

Mirage,  151,  152. 

Miraldf,  M.,  discovers  the  rotation  of 
Jupiter's  fourth  satellite,  65. 

Mifcscherlich,  Professor,  on  crystali- 
zation,  and  the  effect  of  heat  on 
crystaline  bodies,  105,  106.  His 
theory  of  isomorphism,  107.  On  the 
expansion  of  crystaline  bodies,  2--*- 

Molecular  attraction,  9fi. 

Molecule?,  or  ultimate  particles,  101. 

Moll,  Professor,  his  temporary  mag- 
nets, 317. 

Momentum  of  the  planets,  12.  Note 
59. 

Monocotyledonous  plants,  267. 

Monsoons,  118. 

Moon,  theory  of  the,  33. 

,  periodic  and  secular  perturba-  j 

tion  of,  34  et  gtq. 

,  action  of  planets  on,  35. 

disturbs  her  o.vvn  motion,  35. 

,  acceleration  of,  3ii. 

,  periods  of  her  secular  inequal- 1 

ities.  37. 

,  mean  anomaly  of,37.  Note  106.  > 

,  form  of,  64. 

,  mass  of,  55. 

,  rotation  of,  63. 

,  libration  of,  64,  65. 

,  constitution  of,  65. 

,  light  of,  239. 

,  atmosphere  of,  -23,-\ 

,  phases  of,  38. 

,  eclipses  of,  39. 

,  orbit  of,  33. 

,  nutation  of,  38. 

and  earth's  reciprocal  altrac 

tion.  5. 


Moon's  southing.  91.     Note  155. 

Moorcroft,  Mr.,  his  botanical  obser- 
vations, 265. 

Moser's  discoveries,  233. 

Mossotti,  Professor,  his  theory,  97 
et  seq. 

Motion,  mean,  9.    Notes  43,  45. 

,  true,  9.    Note  44. 

of  solar  system,  6. 

of  translation  and  rotation,  6,  7. 

of  solar  perigee,  81. 

of  lunar  perigee  and  nodes,  37. 

of  ether,  350. 

Mundy,  Captain,  his  observations 
on  mirage,  152. 

Musical  sounds,  125. 

instruments,  137  et  seq. 

strines,  vibrations  of,  134  et  seq. 

Note  176. 


Nature,  laws  of,  386. 

Nebula:,  376. 

,  forms  of,  377,  378, 

,  stellar  and  planetary,  379. 

,  constitution  of,  380. 

,  distribution  of,  380. 

Nebulosity  of  comets,  352,  357. 

Nebulous  stars,  379. 

Needle,  the  magnetic,  300. 

— • — ,  the  dipping,  301. 

Newton,  Sir  Isaac,  on  the  attraction 
of  spheroids,  4.  His  discovery  of 
gravitation,  ib.  Of  the  laws  of 
elliptical  motion,  4,  22.  On  the 
figure  of  a  fluid  mass  in  rotation, 
4\\.  His  theory  of  the  tides,  8C. 
His  analysis  of  lisht,  153,  ]54.  His 
theory  of  light,  161.  His  rings, 

165.  *  Mensuration  of  his  rings, 

166.  His  scale  of  colors,  167. 
Nickel,  sulphate  of,  its  properties, 

106.    Note  161. 

X«K!  il  points  of  vibrating  strings  and 
columns  of  air,  134  et  seq. 

lines  in  air,  144. 

lines  on  cylinders,  141. 

lines  on  surfaces,  138. 

Nodes,  ascending  and  descending, 
10.  Note  55. 

,  motion  of,  18.    Note  73. 

connected  with  the  inclination, 

19. 

Norman,  Robert,  discovers  the  mag- 
netic dip,  305. 

Nutation  of  earth's  axis,  76.  Note 
144. 

of  lunar  oibit,  7,     Note  35, 


456 


Nutation,   reciprocal,  of  earth  and 

lunar  orbit,  7.     Note  33. 
,  effects  of,  73. 

O. 


Oblate  spheroid,  4.    Note  9. 
Obliquity  of  the  ecliptic,  9, 21.   Note 

46. 

,  its  variation  and  limits,  23. 

Occupation  of  planets  and  stars,  41.  ! 
Ocean,  tides  of,  85. 

,  effects  of,  on  gravitation,  50. 

,  density  of,  50. 

,  mean  depth  of,  86. 

,  stability  of,  93. 

• ,  currents  in,  95. 

Octahedrons,  105.    Notes  160,  165. 
Oersted,  Professor,  his  discovery  of 

electro-magnetism,  319. 
Olbers,  M.,  his  observations  of  Bie- 

la's  cornet,  347 ;  and  of  the  comet 

of  1811,  353. 
Olmsted,  Professor,  on  the  shooting 

stars  of  the  13th  of  November,  385. 
Opposition,  29.    Note  96. 
Optic  axis  of  a  crystal,  177.    Note 

202. 
Orbit  of  a  plane),  8. 

of  comets,  339. 

of  binary  systems,  365  et  seq. 

of  celestial  bodies,  360. 

— ,  elements  of  an,  10,  57. 
Ordinary  refraction,  148.    Note  184. 

ray,  175. 

Oscillations,  3.    Note  4. 

of  the  ocean,  86. 

of  the  pendulum,  49.    Note  127. 

of  the  atmosphere,  115. 

P. 

Pacific  Ocean,  the  origin  of  the  tides, 

91. 

Pallas,  its  size,  56. 
Parabola,  5.    Note  22. 
Parabolic  elements,  339. 
Parallactic  motion,  370. 
Parallax,  51.    Notes  128,  129. 

,  horizontal,  51. 

of  the  sun,  Mars,  and  Venus, 

52,  53. 

of  the  moon,  51. 

,  annual,  53,  371. 

Parallel  directions,  14.    Note  62. 

of  latitude,  47.    Note  11. 

Parathermic  rays  of  solar  spectrum, 

231 
Parry,  Sir  Edward,  his  journey  on 


the  ice,  95.  On  the  cold  at  Mel- 
ville Island,  241.  On  the  tem- 
perature of  the  Arctic  seas,  260. 

Particles  of  matter,  4,  96.     Note  6. 

subject  to  gravitation,  4,  100. 

,  size  of,  101. 

,  relative  weights  of,  102. 

,  form  of,  104. 

Pendulum,  32,  49.    Note  100. 

,  its  variation  discovered,  50. 

Penumbra,  39.    Note  111. 

Perigee,  lunar,  34.    Note  102. 

,  variation  of,  37. 

,  variation  of  solar.  82.    Note 

147. 

Perihelion,  10.    Note  57. 

,  secular  variation  of,  16.     Note 

64. 

Periodic  inequalities  of  the  planets, 
13. 

of  Jupiter's  satellites,  27. 

of  the  moon,  34. 

times,  5,  9. 

,  proportional  to  cubes  of  mean 

distances,  5.     Note  20. 

Periodicity  of  the  planetarv  pertur- 
bations, 20. 

Periods  of  rotation  of  the  celestial 
bodies,  61  ct  seq. 

Perkins,  Mr.,  his  experiments  on  the 
compressibility  of  matter,  74. 

Peron  and  Lesueur,  MM.,  on  the  dis- 
tribution of  marine  animals,  269. 

Perturbations  of  the  planets,  peri- 
odic and  secular,  12,  13. 

expressed  in  sines  and  cosines 

of  circular  arcs,  20.     Note  7(5. 

of  Jupiter  and  Saturn,  24. 

of  Venus  and  the  earth,  25. 

of  Jupiter's  satellites,  27. 

of  the  moon,  33,  34. 

of  comets,  338. 

Phases  of  the  moon,  38. 

Phosphorescence,  28(5. 

Phosphorescent  action  of  solar  spec- 
trum, 286. 

Photographic  rays  of  solar  spectrum, 
194  ct  seq. 

pictures,  197. 

Plane  of  ecliptic,  9. 

,  its  secular  variation,  21. 

Planetary  motions.  8,  13. 

Planets  move  in  conic  sections,  o. 

,  their  forms,  4, 

,  atmospheres  of,  238. 

,  constitution  of,  240. 

Plants,  their  distribution,  262  ct  seq 

Plateau,  M.,  on  complementary  col 
ors,  160. 


INDEX: 


I. 37 


Platina,  spontaneous  combustion  of, 
104. 

Poinsot,  M.,  on  the  invariable  plane, 
23. 

Poisson,  Baron,  his  researches  on 
capillary  attraction,  109.  On  the 
distribution  of  the  electric  fluid, 
276.  On  the  law  of  the  magnetic 
force,  308,  309. 

Polar  star,  77. 

Polarization  of  light,  172 

by  refraction,  173. 

by  reflection,  178.    Xote  205. 

,  circular,  183  et  seq.    Note  209. 


R. 

Radial  force,  7. 
Radiation,  221  et  seq. 

of  the  earth.  -251. 

of  the  sea,  256. 

,  solar,  68,  261.    Note  140. 

Radii  vectores,  8.    Note  40. 
Radius,  4.    Note  15. 
,  terrestrial,  polar,  and  equato- 
rial, 47. 

,  solar,  56. 

vector,  14. 

Raffles,  Sir   Stamford,  his  account 


of  the  volcanic  irruption  at  riaou- 

ba\va,  247. 
Rain,  2-22. 

Ratio,  4,  5.    Note  16. 
Rays  of  Light,  148. 


in  quartz,  183,  187. 

,  interference  of,  168.    Note  211. 

Polarizing  angles,  179.     Note  205. 

apparatus.     Note  206. 

Poles  of  rotation,  4.    Note  11. 


elliptical,  187. 

,  discovery  of,  189. 

of  heat,  2"l5. 

,  circular,  of  heat,  217. 

Polarized  light,  173. 

,  undulations  of,  176, 188.    Note   of  heat,  208 

201.  i ,  chemical,  193  et  seq. 

,   phenomena    of,    180  et  seq.    ,  extraordinary    and    ordinary, 

Notes  -207,  208.  !      177. 

i  Reflection  of  light.    Notes  184,  198. 
— ,  extraordinary  and  total.   Note 
i      184. 

of    sound,    131.     Notes    174, 

175. 

of  celestial  equator,  orequinoc-    of  waves,  131.    Note  174. 

rial,  and  of  ecliptic,  9,  76.    Note    Refraction  of  light,  148,  149,  171. 
46.  i      Notes  184,  198. 

of  maximum  cold,  260.  ,  atmospheric,  148.     Note  185. 

,  magnetic.  300.  i in  eclipses,  39. 

Pouillet,  M.,  his  estimation  of  the  i ,  terrestrial,  150.    Note  187. 

quantity  of  heat  annually  received    .  extraordinary,  150.   Notes  188, 

from  the  sun,  251,  252!    On  the  i      189. 
production  of  atmospheric  elec-  '  Repulsive  force,  96. 
tricity,  281.  Resisting  medium,  and  its  effects, 

Powell,  Professor,  on  the  dispersion       21,  162,  163,  346.    Note  78. 
of  light,  191.     His  experiments  on  i  Resonance,  144. 
heat,  213.  i  Retrograde  motion,  13.    Note  61. 

Precession  and  nutation,  74.    Notes    Revolution,  sidereal,  of  planets,  16. 
143,144.  Notefi«. 

,  effects  of,  75,  77.  ,  tropical,  16.    Note  69. 

Principal  axis  of  rotation,  71.  ,  synodic,  39.    Note  112. 

Prism,  its  use.  153.  154.  and  rotation  of  the   celestial 

Prismatic  colors.  154.  bodies  in  the  same  direction,  61. 

Probabilities,  theory  of,  its  utility,  59.    Rhombohedron,  175.    Note  200. 
Problem  of  the  three  bodies,  11.          Richman,  Professor,  killed  by  light- 
nine,  383. 

Richter,  his  observations  on  the  pen- 
dulum at  Cayenne,  51. 
Rings,  Saturn's,  62. 

Quadrant  of  the  meridian,  84.   Note  ,  colored,   round,   small    aper- 

151.  tures,  168. 

Quadratures,  9.     Note  51.  — .  Newton's,  165.     Note  194. 

Quadrupeds,  their  distribution,  270.  \  Ritchie,  Professor,  causes  water  to 
Quart/,  or  rock  crystal,  its  proper -I      rotate,  316.    On  the  composition 
ties,  177,  183,  187.  I     of  water  by  magnetic  action.  335. 


Projected,  5.    Note  20. 
Q. 


458 


Ross,  Capt.  James,  his  determination 
of  the  magnetic  pole,  300. 

Rotation  of  the  sun  and  planets,  7, 
(iO,  61. 

of  a  fluid  mass,  6,  43. 

oft  lie  earth,  58,  (56. 

,  invariability  of  the  earth's-,  73. 

of  the  moon,  03. 

of  Jupiter's  satellites,  05. 

of  Saturn's  rings,  62. 

of  winds,  118,  119. 

of  water  by  electricity,  316. 

of  magnets,  315. 


S. 

Sabine,  Colonel,  on  the  magnetic 
equator,  302. 

Salt  and  sugar,  their  capillary  at- 
traction, 110. 

,  rock,  highly  permeable  to  heat, 

209,  211. 

Satellites,  7.     Note  32. 

of  Jupiter,  their  theory,  26. 

of  Saturn  and  Uranus,  32. 

Saturn  and  his  rings,  62. 

Saussure,  M.,  on  the  temperature  of 
mines,  242,  243. 

Savart,  M.,  his  experiments  on  the 
sense  of  hearing,  126.  On  the 
vibration  of  elastic  bodies,  141  et 
scg. 

Savary,  M.,  the  first  who  determined 
the  orbit  of  a  binary  star,  367. 

Schroeter,  M.,  on  the  atmosphere  of 
Ceres,  238. 

Scoresby,  Capt.,  on  extraordinary 
refraction,  151.  On  the  tempera- 
ture of  the  Arctic  regions,  260. 

Seasons,  variation  of,  82. 

Secular  variations,  13. 

of  apsides,  16.     Notes  66,  67. 

of  eccentricity,  19.    Note  70. 

of  the  eccentricity  of  the  ter- 
restrial orbit,  17. 

— —  of  nodes,  18  et  seq.     Note  73. 

of  inclination,  20.  Notes  72, 

75. 

in  the  obliquity  of  the  ecliptic, 

21.  Notes  79,  143,  148. 

of  Jupiter,  19. 

of  Jupiter's  satellites,  27. 

of  the  moon,  35. 

Seebeck,  Professor,  on  the  maximum 
point  of  heat  in  the  solar  spec- 
trum, 215. 

Shell-fish,  the  weight  thev  sustain, 
112. 

Shooting  stars,  382. 


Sidereal  day,  77. 

revolution,  16. 

astronomy,  361. 

I  Sine  of  an  arc  or  angle,  20.   Note  76. 
;  Sinus,  distance  and  light  of,  362. 

Smyth,  Capt.,  measures  the  height 
j      of  Etna,  113.     His  observations  of 
Y  Virgiuis,  368. 

Snow,  line  of,  perpetual,  251. 

Solar  System,  its  motion  in  space,  5, 
|      23,  370. 

!  Solar  spectrum,  154,  156,  192  214. 
I  Solar  heat,  quantity  of,  2.52. 

I ,  distribution  of,  253. 

1  Solstices,  81.    Note  148. 
1  Sothaic  period,  80. 

Sound,  theory  of,  122,  123. 

,  undulations    producing,    124 

Note  156. 

| ,  intensity  of,  125,  131. 

i ,  velocity  of,  129. 

i ,  transmission  of,  123  et  seq. 

! ,  reflection  of,  131,  132. 

,  refraction  and  interference  of, 

'      133. 

Sounds,  musical,  134. 

,  harmonic,  136. 

Space,  5.    Note  21. 

,  temperature  of,  241. 

Speaking-machine,  147. 

Sphere,  attraction  of,  4. 
i  Spheroid,  4.    Note  9. 

| ,  attraction  of  a,  4.     Note  12. 

i  Spring,  22. 

tides,  89. 

i  Square  of  distance,  5.     Note  23. 
I of  moon's  distance,  5. 

—  of  sine  and  cosine  of  latitude, 
45.     Note  123. 

! number  and  its  root.    Note  132. 

!  Stability  of  system,  21. 
I  Stars,  fixed,  361. 

,  parallax  of,  53. 

I ,  distance  of,  53,  370. 

— ,  distances  of,  known  from  the 

binary  systems,  370. 

— ,  number  of,  361. 

— ,  size  of,  362. 

—  that  have  vanished,  and  new 
stars,  363. 

— ,  variable,  36-1. 

,  their  proper  motions,  369,370. 

,  double,  365. 

,  parallactic  motions  of,  370. 

,  binary  systems  of,  and  their 

orbits,  367  et  seq. 

,  color  of,  374. 

- — ,  clusters  of,  374. 
Steam,  227  ct  seq. 


459 


Striive,  Professor,  on  the  rings  of 
Saturn,  63.  On  Halley's  comet, 
343.  On  the  double  stars,  3(58. 

Sun,  the  center  of  gravitation,  5,  6. 

,  motion  of,  8,  370. 

,  magnitude  of,  35. 

,  eclipses  of,  40. 

,  parallax  and  distance  of,  58. 

,  mass  of,  55. 

,  rolatitm  of,  61. 

,  constitution  of,  238,  239. 

,  light  and  atmosphere  of,  239. 

,  spots  on,  239. 

.  heal  of,  251,  252. 

Surfaces  vibrating.  137. 

Svanberg,  M.,  on  the  temperature 
of  space,  240. 

Sykes,  Col.,  on  the  height  at  which 
wheat  grows,  264. 

Synodic  revolution,  39.     Note  112. 

Syren,  138. 

Syrup,  physical  properties  of,  184. 

System,  Solar,  its  stability,  21. 

,  its  motion,  6,  370. 

of  Jupiter  and  his  satellites,  27. 

of  binary  stars,  367. 

Syzygies,  88.    Note  153. 

T. 

Tangent,  8  Note  38. 
Tangential  force,  15. 
Temperature,  internal,  of  the  earth, 

67,  242. 

,  stratum  of  mean,  241. 

of  mines,  242. 

of  wells,  243. 

of  ocean,  -J4.J. 

,  superficial,  of  earth,  249. 

,  eflfects  of,  on  vegetation,  262. 

of  space,  241. 

of  the  sun,  moon,  and  planets, 

<*38etseq.. 
Terrestrial  latitude  and  longitude,  4. 

Note  IT. 

meridian,  45. 

refraction,  150. 

imgnetism,  300,  333. 

Tessuiar  system,  107. 
Tetrahedron,  107.     Note  164. 
Theory  of  Jupiter's  satellites,  26. 

of  the  moon,  33. 

of  the  tides?,  85. 

,  atomic,  101. 

of  sound,  122. 

of  light,  148  et  seq. 

of  heat,  206. 

of  electricity,  271  et  sr.q. 

Thermal  springs,  252. 


!  Thermo  electricity,  328. 
;  Thermo  multiplier,  329. 

Thunder,  132. 

Tides,  theory  of,  86. 

,  semi-diurnal,  87, 

— — ,  semi-annual,  89. 

,  effects  of  declination  on,  90. 

Note  154. 

1 ,  neap  and  spring,  89. 

; .height  of,  89,  91. 

,  propagation  of,  90. 

! ,  forces  producing,  92. 

i at  Batsha,  93. 

!  Time,  mean  and  apparent  solar,  78. 

,  mean  and  apparent  sidereal, 

, ,  equinoctial,  81. 

,  equation  of,  78. 

| ,  square  of,  36.    Note  105. 

,  divisions  of,  79. 

Timocharis,  his  observations,  75. 

Torpedo,  its  electric  properties,  299. 

Tourmaline,  its  properties,  173,  176, 
17*.    Note  199. 

Trade  winds,  116.          ..  ".* 

Transit  of  Venus,  52.     Note  131. 
I  Transmission  of  light,  171.    . 
' of  undulations,  123. 

of  sound.  129. 

of  heat,  208. 

Translation,  7.    Note  3(5. 

Triangulation,  46.    Note  125. 

Tropical  revolution,  16.    Note  69 
j  Tuning-fork,  experiment  with,  133. 

U. 

Undulations  of  water,  92,  93.    Note 
156. 

i of  air,  illustrated  by  those  of  a 

!     field  of  corn,  123. 

. of  air,  124. 

of  ether,  illustrated  by  those  of 

a  cord,  164, 186,  187. 

,  small,  115. 

Undulatory  theory  of  light,  161  et  seq. 

,  his  distance  from  the  sun,  53. 

,  hia  satellites,  32. 

Universe,  23,  381. 

V. 

Va'.z,  M.,  on  Halley's  comet,  343. 
On  the  nuclei  of  comets,  358. 

Vapor,  -2-iS. 

Variation,   a   lunar  inequality,  34. 
i      Note  104. 
| of  the  compass,  300  ct  seq. 


IMDKX. 


Varieties  of  mankind,  270. 
Vegetation,  262. 
Velocity  of  light,  31. 

of  electricity,  284. 

,  comparative,  369. 

of  the  gravitating  force,  386. 

Venus,  her  action  on  the  earth,  25. 

,  her  nodes,  13,  52. 

,  transit  of,  52. 

,  climate  of,  240. 

Vibrations  of  musical  strings,  134. 

of  columns  of  air  in  pipes,  137. 

of  elastic  solids,  138  et  seq. 

sympathetic,  1,  142. 

of  polarized  light,  176.  Note  201. 

Volcanic  action,  246. 

,  theories  of,  249. 

Volta,  Professor,  his  construction  of 

the  Voltaic  pile,  290. 
Volta-electric  induction,  323. 
Voltaic  battery,  292. 
electricity,  discovery  of,  290. 

properties  of,  294. 

luminous  effects  of,  295. 

chemical  effects  of,  296. 

transference  of,  297. 

composition  by,  297. 

effects  of,  on  the  senses,  299. 

Volume,  56. 

W. 

Water,  decomposition  and  compo- 
sition of,  296,  328,  336. 

of  crystiilization,  105. 

a  conductor  of  sound,  129. 

,  rotation  of,  316. 

Week,  the  antiquity  of,  80. 

Weigh!  of  the  atmosphere,  112. 

decreases  from  the  poles  to  the 

equator,  44,  49. 


Weight  at  the  surfaces  of  the  sun 
and  planets,  56. 

Weights  and  measures,  84. 

Wheatstone,  Professor,  his  musical 
instruments,  138.  His  experiments 
on  vibrating  surfaces,  140.  On  the 
transmission  of  sound,  145.  On  re- 
sonance, 146.  On  the  velocity  of 
the  electric  fluid,  284.  On  the 
spectrum  of  theVoltaic  spark,  295. 

Willis,  Mr.,  his  speaking-reed,  147. 

Wollaston,  Dr.,  on  the  extent  of 
the  atmosphere,  101.  On  the  ex- 
tent of  hearing,  125.  On  refrac- 
tion, 151.  Discovers  the  chemical 
rays  and  dark  lines  of  the  solar 
spectrum,  157,  194.  On  rotatory 
motion  by  the  electro-magnetic 
force,  315.  On  the  light  of  the 
celestial  bodies,  362. 

Y. 

Year,  civil  or  tropical,  and  sidereal 
years,  77  et  seq. 

Young,  Dr.  Thomas,  on  the  compres- 
sion of  substances,  73.  His  hiero- 
glyphic researches,  84.  On  capil- 
lary attraction,  109.  On  the  love 
of  harmony,  136.  Establishes  the 
undulatory  theory  of  light,  163. 
On  the  interference  of  light,  169. 
On  radiant  heat,  230. 

Z. 

Zodiacal  light,  supposed  to  be  the 
atmosphere  of  the  sun,  379;  or, 
according  to  La  Place  and  Profes- 
sor Olmsted,  a  nebulous  body  re- 
volving in  the  plane  of  the  solar 
equator,  385. 


THE  END 


HARPER'S   NEW   MISCELLANY 

OF 

POPULAR  STERLING  LITERATURE. 

"  Books  that  have  an  at'm  and  meaning  in  them." 

Now  in  course  of  publication,  a  new  and  attractive  library 
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PRICE   FIFTY   CENTS  A  VOLUME. 

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Clements  of  Morality  and  Polity. 

BY    WILLIAM    WHEW  ELL,     D.D. 

AUTHOR    OF    "HISTORY    AND    PHILOSOPHY    OF    THE     INDUCTIVE     SCIEN- 
CES,"  &C. 

2  vols.  12mo,  Muslin,  extra  gilt,  $1  00. 

Dr.  Whewell's  work  ought  to  be  read,  because  it  can  not  be  read  without 
advantage  :  the  age  requires  such  books.  —  London  Athenaeum. 

A  text-book  of  simple  truths,  from  which,  by  induction,  a  complete  sys- 
tem of  morality  is  constructed,  applicable  to  all  the  relations  and  circum- 
stances of  life,  and  embracing  every  department  of  human  action.  The 
reader  who  shall  carefully  study  these  volumes  —  and  a  more  inviting  page, 
clear  and  legible,  the  eye  does  not  often  rest  upon  —  will  find  his  labor  more 
than  rewarded.  —  New  York  Commercial  Advertiser. 

Professor  Whewell's  "  Elements  of  Morality"  have  been  universally  re- 
ceived in  England  as  a  contribution  of  rare  value  to  the  department  of  moral 
and  political  science.  —  Baltimore  American. 

A  splendid  production  by  one  of  the  most  distinguished  of  the  scientific 
men  of  the  age.  This  is  a  book,  not  to  be  read  merely,  but  to  be  re-perused 
and  patiently  studied  ;  we  have  heard  it  pronounced  "by  no  mean  critic  the 
most  complete  aud  lucid  work  on  ethical  philosophy  ever  produced.  We 
commend  this  work  to  the  especial  notice  of  thinkers  and  readers,  to  schol- 
ars and  schools  generally,  as  a  most  admirable  text-book.  —  Sun. 

The  style  of  the  work,  though  simple,  is  extremely  clear,  strong,  and  el- 
oquent. It  is  a  book  to  be  studied  rather  than  superficially  read,  and  can 
not  fail  to  be  of  the  very  highest  importance  in  instructing  and  disciplining 
the  public  mind.  —  American  Patriot. 

This  is  beyond  all  comparison  the  most  complete,  comprehensive,  and  lu- 
minous treatise  on  the  important  subjects  it  discusses,  that  is  to  be  found 
in  the  language,  and  its  careful  study  is  indispensable  to  every  one  who 
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and  private  morals.  It  is  profoundly  learned  and  philosophical,  but  the  writ- 
er thinks  logically  and  clearly,  and  is  therefore  at  all  times  lucid  and  com- 
prehensible.— Buffalo  Commercial  Advertiser. 


2  HARPER'S  NEW  MISCELLANY 

in. 
The  Philosophy  of  Mystery. 

BY    WALTER    COOPER     D  E  N  D  Y. 

12mo,  Muslin,  extra  gilt,  50  cents. 

This  is  a  learned  and  elaborate  work,  in  which  the  writer  goes  into  the 
investigation  of  all  the  phenomena  of  mind  in  the  erratic  operations  and 
phantasies  of  ghost  seeing  and  spectral  hallucinations,  and  aims  to  give  the 
true  philosophy  of  all  such  delusions.  He  is  a  medical  man  of  consider- 
able eminence,  and  has  spared  no  pains  in  his  researches,  giving  a  great 
number  of  facts  and  cases  to  illustrate  his  philosophy.  The  volume  will  be 
much  sought  for,  as  it  is  really  a  desideratum  in  the  world  of  literature. 
We  know  of  no  work  on  this  subject  which  lays  the  same  just  claim  to  public 
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ular time,  when  the  extremes  of  superstition  and  philosophy  have  shaken 
hands,  it  will  be  likely  to  effect  an  inconceivable  amount  of  good,  if  prop- 
erly studied.  It  is  one  of  the  most  remarkable  productions  of  the  day,  and 
must  create  an  extraordinary  degree  of  interest  in  the  public  mind. — .Ifer- 
chant's  Magazine. 

It  belongs  to  that  class  of  writings  which  you  can  take  up  and  put  down 
at  pleasure,  and  which  may  be  subjected  to  repeated  readings.  The  woik 
is  pleasant,  however,  in  spite  of  this — pleasant  because  of  its  facts,  its  nu- 
merous details  of  mystery,  its  vast  collection  of  anecdote,  its  developments 
rf  diablerie,  its  tidings  from  the  spiritual  world,  and  the  many  cases  which 
ii  brings  together  of  the  curious  and  the  wonderful  in  nature  and  art,  which 
former  ages,  and  ignorance  and  superstition,  have  concluded  to  consider  su- 
pernatural. Where  science  and  modern  speculation  furnish  the  solution  to 
the  mystery,  Mr.  Dendy  couples  it  with  the  statements,  and  the  book  is 
thus  equally  valuable  and  amusing. — Charleston  Transcript. 

Here  lies  a  remarkable  work  ;  beautiful  in  its  style,  and  wondrous  in  its 
matter.  The  work  is  strictly  philosophical  in  its  tendency,  yet  more  amus- 
ing than  a  novel. —  True  American. 

This  is  a  book  for  the  lovers  of  marvels  and  of  mysteries.  It  contains  an 
immense  collection  of  anecdotes  of  spectral  apparitions,  of  illusions  of  vision 
or  of  hearing,  of  striking  phenomena  exhibited  in  dreams,  in  insanity,  in 
trance,  or  in  magnetism,  and  furnishes  many  very  valuable  hints  to  aid  in 
the  solution  of  these  mysteries,  by  which  so  many  have  been  bewildered 
or  affrighted.  It  is  written  in  a  style  of  great  ease  and  elegance,  and  can 
not  fail  to  find  a  very  wide  circle  of  welcoming  readers. — Albion. 

This  unique  and  remarkable  book  has  just  been  placed  on  our  table  ;  we 
know  its  reputation  of  old  ;  it  is  an  admirable  discourse  on  the  subject  of 
supernaturalisms,  such  as  mental  illusions,  dreams,  ghosts,  mesmeric  phe- 
nomena, &c.  If  any  one  will  but  read  the  first  half  dozen  pages,  we  will 
vouch  for  it  he  will  not  neglect  the  rest  of  the  volume  :  it  is  one  of  the  best 
written  books  on  one  of  the  most  curious  range  of  topics  that  could  engage 
the  pen  of  a  writer,  or  the  attention  of  a  reader.  It  is,  in  fact,  one  of  the 
most  curious  volumes  ever  perused,  upon  a  series  of  the  most  singular  sub- 
jects, and,  in  this  new  and  ueat  form,  it  will  command  a  vast  number  of 
readers. — Sunday  Times. 

"The  Philosophy  of  Mystery"  is  an  exceedingly  able  work  ;  far  better, 
we  think,  than  the  "  Natural  Magic"  of  Brewster,  a  book  of  identical  pur- 
pose, carried  out  in  a  totally  different  way.  The  "  Natural  Magic"  is  the 
more  ratiucinative,  Mr.  Dendy's  essay  the  inon1  poetical,  the  more  imagina 
tii'e,~and  to  us  the  i,u>re  interesting  '-- Xaticn*?  PrfSf. 


OF    POPULAR    STERLING    LITERATURE.  3 

The  Life  of  Mozart: 

INCLUDING    HIS    CORRESPONDENCE. 
BY    EDWARD    HOLMES, 

AUTHOR  OF  "  A  E AMBLE  AMONG  THE  MUSICIANS  OF  GERMANY,"  &C. 

12mo,  Muslin,  extra  gilt,  50  cents. 

It  is  written  in  a  beautiful,  narrative  style,  and  can  not  but  be  every 
where  acceptable.  To  all  who  appreciate  the  extraordinary  genius  of  Mo- 
zart, the  delicate  structure  of  his  mind,  the  incidents  of  his'life,  and  his  ro- 
mantic death,  this  volume  will  indeed  be  a  treasure.— Bottom  Gazette. 

It  contains,  in  addition  to  much  of  his  interesting  correspondence,  and 
other  papers,  a  detailed  account  of  his  life,  adventures,  and  rise  as  an  artist, 
and  a  discriminating  sketch  of  his  character,  the  peculiarities  of  which  are 
happily  illustrated  by  anecdotes.  Many  things  of  him,  unknown  even  to 
his  admirers,  are  here  given  to  the  world,  and  his  biographer,  fully  appre- 
ciating the  artist,  has  yet,  not  like  a  flatterer,  but  with  true  independence, 
spoken  candidly  of  the  faults  of  the  man.— Jfercfcoit'*  Magazine. 

Of  this  far-famed  life  of  Mozart  it  M  scarcely  necessary  for  us  to  say  a 
word ;  the  foreign  reviews  have  been  so  unanimous  in  their  encomiums, 
that  we  suppose  few  will  be  found  insensible  to  the  strong  inducement  of 
its  perusal,  especially  as  the  work  may  be  obtained  at  the  trifling:  cost  of 
half  a  dollar,  and  in  so  beautiful  a  guise.  We  have  looked  into  the  biog- 
raphy but  slightly,  yet  find  it  redolent  with  interest,  and  fully  sustaining 
the  high  estimate  placed  upon  the  work  by  the  London  Atken**m  and 
BlmcJaeood.  If  the  Harpers  continue  to  nil  their  new  library  with  sterling 
works  like  the  present,  it  will  present  the  most  truly  valuable  series,  yet 
the  cheapest,  ever  attempted  in  any  age  or  country. — Evening  Gazette. 

The  only  authentic  biography  of  the  great  composer  that  is  extant  in  the 

1  the  events  of  his  care 

monitions  and  warning  to  the  sons  of  genius,  and  they  whisper  to  those 
!  not  allowed  that  there  is  a  future  full  of  promise. 


English  language,  and  the  events  of  his  career  are  replete  with  useful  ad- 

d w 

wose  present  clams  are  not  aowed  tat  there  is  a  future  ul  o  promise. 
In  his  life  Mozart  was  neglected  and  impoverished,  and  he  went  to  his 
grave  with  more  than  the  bitterness  of  death  crowding  on  his  thoughts, 
but  fame  has  taken  possession  of  his  memory,  and  among  those  who 


as  gods  in  musical  art,  few  are  equal  to  him,  none  are  superior.    This  bi- 
ography possesses  an  interest  for  all  who  feel  interested  in  the  great  men 
of  the  earth.    It  is  not  only  remarkably  well  written,  but  has  a  complete- 
ness about  it  we  have  never  found  before  in  any  life  of  Mozart.  -  LmtitviUe 
torn*. 

There  is  such  a  charm  in  this  narrative,  that  the  lovers  of  good  biography 
can  not  hear  of  it  too  soon.    We  can  not  conceive  a  more  fascinating  story 
of  genius.     To  a  style  which  would  alone  have  sufficed  to  the  production 
of  an  interesting  and  striking  narrative,  Mr.  Holmes  unites  a  depth  of 
1  ------  '  *—  i  and  musical  appreciation  very  rare  and  remarkable.     W«  thank 

for  a  most  pleasing  addition  to  our  standard  biographical  lit- 

The  book  is  one  of  extraordinary  interest,  not  merely  to  the  lovers  of 
music  and  appreciators  of  the  great  'composer,  but  to  the  general  reader,  as 
a  vivid  picture  of  the  life  of  a  man  of  genius,  who  encountered  all  the  dif- 
ficulties, trials,  and  sufferings  usually  the  lot  of  genius  when  it  comes  be- 
fore a  world  incapable  of  appreciating  it,  and  indifferent  to  its  welfare.  The 
domestic  portions  of  the  book  are  invaluable  ;  his  relations  to  has  father  and 
his.  wife  are  very  beautiful.  The  work  is  admi  rablj  executed,  as  we',]  in  the 
scientific  as  anecdotical  passages,  and  is  worthy  of  the  widest  sale.—  .Veic  5. 


4  HARPER  3    NEW    MISCELLANY 

V. 

The  Practical  Astronomer: 

COMPRISING  ILLUSTRATIONS  OF  LIGHT  AND  COLORS; 
PRACTICAL  DESCRIPTIONS  OF  ALL  KINDS  OF  TEL- 
ESCOPES, &C.,  WITH  DESCRIPTIVE  ACCOUNTS  OF 
THE  EARL  OF  ROSSE's  LARGE  TELESCOPES,  AND 
OTHER  TOPICS  CONNECTED  WITH  ASTRONOMY. 
BY  THOMAS  DICK,  LL.D., 

A.UTHOR  OF  THE  "CHRISTIAN  PHILOSOPHER,"  "  CELESTIAL  SCENERY." 
"THE  SIDEREAL  HEAVENS,"  &r. 

100  Engravings.     12mo,  Muslin,  extra  gilt,  50  cents. 

The  name  of  the  distinguished  author  of  this  work  is  a  sufficient  pass- 
port to  public  favor  and  a  sure  guarantee  to  its  sterling  value,  and  those 
who  have  read  Dr.  Dick's  former  works  will  need  no  recommendation  of 
this  book  by  us.  He  is  not  only  an  original  and  profound  observer  of  na- 
ture, but  truly  a  most  excellent  Christian  philosopher,  whose  powers  of  in- 
tellect and  expanded  views  of  the  character  of  the  great  Architect  of  the 
universe  are  so  eminently  calculated  to  direct  the  mind  not  alone  to  the 
grandeur,  the  magnificence,  and  sublimity  of  the  laws  and  principles  of 
the  material  world,  but  to  look  through  nature  up  to  "  Nature's  God.''  It 
is  truly  a  valuable  work. — Farmer  and  Mechanic. 

The  merits  of  this  work  are  of  the  highest  order;  Dick  is  one  of  the 
profoundest  and  purest  of  modern  philosophers. —  Western  Continent. 

Here  is  the  ninth  volume  presented  by  this  gifted  author  to  the  public  ; 
he  aim  of  all  of  which  has  been  to  simplify  sciences  which  before  have 
been  too  often  considered  as  every  way  above,  and  therefore  unworthy  of 
the  attention  of  ordinary  readers.  It  is  specially  addressed  to  private  stu 
dents  and  the  higher  schools,  and  comprises  a  large  amoUnt  of  new  and 
valuable  matter  connected  with  astronomy,  and  pointing  out  ways  in  which 
the  more  humble  student  can  in  the  best  way  improve  the  advantages  placed 
in  his  way. — Auburn  Journal. 

Let  not  the  inquisitive  fear  that  the  intricacies  qf  science  or  the  techni- 
calities of  language  will  obstruct  the  pleasure  they  will  derive  from  the 
study  of  this  book  ;  for  the  clearness  of  the  author's  style,  and  the  elucida- 
tion of  the  one  hundred  engravings,  render  it  within  the  scope  and  compre- 
hension of  every  intelligent  student. — Industrial  Record. 

The  copious  use  of  engravings  and  of  pictorial  illustrations,  together  with 
the  plain,  popular  explanations,  render  this  book  a  truly  practical  work. 
Dr.  Dick  is  not  only  thoroughly  scientific,  but  he  knows  well  how  to  render 
his  acquisitions  available  to  the  great  body  of  common  readers,  by  his  ac- 
curate method  and  clear  descriptions. —  Watchman. 

We  have  always  been  an  admirer  of  the  writings  of  this  gentleman,  and 
popularity  keeps  on  his  side  wherever  he  is  known.  He  is  a  profound 
thinker  and  a  devout  Christian.  His  works  all  tend  to  illustrate  the  simple 
as  well  as  the  sublimest  principles  of  philosophy,  and  while  they  instruct, 
can  not  fail  to  enlighten.  The  present  volume  comprises  illustrations  or 
light  and  colors,  practical  descriptions  of  all  kinds  of  telescopes,  the  use  of 
the  equatorial-transit,  circular,  and  other  astronomical  instruments,  and 
other  topics  connected  with  astronomy.  It  is  illustrated  by  100  engrav- 
ings, and  will  be  found  a  most  valuable  book  for  all  classes,  but  particularly 
as  a  work  of  instruction  for  youth.— Illustrated  Magazine. 


OF    POPULAR    STERLING    LITERATURE. 


The  Life  of  Paul  Jones. 

BY   ALEXANDER  SLIDELL   MACKENZIE,   U.S.  N. 
2  vols.  12mo,  Portrait,  Muslin,  extra  gilt,  81  00. 

The  history  of  the  naval  adventures  and  victories  of  Paul  Jones  forms  one 
of  the  most  romantic  chapters  in  the  record  of  great  deeds,  and  can  not  fail 
to  attract  general  and  ardent  attention,  since  it  relates  to  the  very  beginning 
of  the  American  navy.— Commercial  Advertiser. 

The  various  biographies  of  Paul  Jones  now  extant  have  been  carefully 
searched  by  Mr.  Mackenzie;  as  also  the  log  books  of  Jones's  various  cruiz- 
es and  papers  in  possession  of  his  heirs,  with  a  view  to  procure  a  full  an<* 
authentic  collection  of  facts  and  incidents  for  the  present  work.  Thus  in 
dustriously  compiled  and  stored,  and  that  by  au  able  hand,  this  edition  must 
necessarily,  as  it  does,  possess  considerable  merit. — Philadelphia  Chronicle 

Paul  Jones  will  always  be  regarded  as  one  of  the  most  daring  and  gallant 
heroes  who  ever  made  the  ocean  the  theater  of  their  exploits.  Such  a 
name  can  never  be  forgotten  by  Americans,  nor  can  the  services  which  he 
rendered  to  the  cause  of  American  liberty,  in  its  infant  struggles,  ever  pass 
into  oblivion.  No  better  biographer  for  such  a  character  could  have  been 
found  than  Captain  Mackenzie.  Familiar  with  all  the  details  of  seaman- 
ship, possessing  the  same  bold  patriotism  which  made  the  career  of  his  hero 
so  illustrious,  and  being  an  accomplished  and  vigorous  writer,  he  has  given 
us  a  most  admirable  biography. — Courier  and  Enquirer. 

This  is  a  capital  American  biography,  of  an  American  naval  hero,  scarcely 
less  renowned  and  no  less  gallant  and  gifted  with  an  heroic  spirit  than  Nel- 
son, the  great  British  admiral.  There  is  scarcely  a  more  stirring  life  in 
the  whole  compass  of  literature  than  that  of  Jones  ;  and  the  important  part 
he  played  in  giving  force  and  almost  life  itself  to  the  American  navy,  then 
in  its  earliest  infancy,  renders  his  history  peculiarly  interesting  and  attract 
ive.  No  man  certainly  ever  performed  more  gallant  exploits,  and  few  have 
rendered  more  important  service  to  the  cause  of  freedom  than  he.  Many 
of  his  actions  for  bravery,  skill,  and  the  performance  of  almost  incredible 
deeds,  by  apparently  the  most  inadequate  njeans,  are  scarcely  rivalled  by 
any  thing  in  the  records  of  naval  history.  His  life  should  be  familiar  to 
American  readers;  and  in  the  elegant,  forcible,  and  graphic  style  of  Com- 
mander Mackenzie  it  can  not  fail  to  be  universally  read. — True  Sun. 

We  are  elad  to  see  the  life  of  this  celebrated  man  by  one  competent  to 
write  it.  His  adventures  border  so  much  on  the  marvelous  that  one  is  glad 
to  be  sure  of  reading  only  what  is  authentic,  and  that  written  in  a  style  and 
language  becoming  the  subject.  There  is  a  good  moral  lesson  conveyed  in 
this  life  of  Paul  Jones. — Christian  Advocate  and  Journal. 

The  name  and  achievements  of  Paul  Jones  are  indissolubly  connected 
with  American  history;  and  his  renowned  deeds,  which  made  him  the  ter- 
ror of  the  coast  of  Britain,  are  among  the  most  romantic  in  the  annals  ot 
naval  warfare,  and  impart  to  this  work  the  highest  interest.  This  is  the 
most  complete  and  authentic  biography  of  Commodore  Jones  ever  published, 
as  all  accessible  materials  have  been  collected,  and  are  used  by  Commander 
Mackenzie  with  the  ability  and  tact  which  he  possesses  as  an 'accomplished 
scholar  and  an  officer,  accomplishments  which  peculiarly  qualify  him  to 
write  naval  biography.  A  fine  portrait  of  this  true  naval  hero  will  be  found 
in  the  first  volume. — Baltimore  American. 

We  have  read  it  with  some  care,  and  compared  it  with  other  biographies, 
and  think  it  greatly  superior  to  any  yet  published.  It  contains  a  full  nar- 
rative of  all  the  important  events  in  Jones's  eventful  career,  and  yet  is  less 
voluminous  than  previous  works. — Highland  Courier. 


6  HARPER'S    NEW    MISCELLANY 

VIII. 

The  Ascent  of  Mount  Ararat, 

(ACHIEVED   FOR    THE   FIRST    TIME). 

BY    DR.    FRIEDRICH     PARROT. 

TRANSLATED  BY  W.  D.  COOLEY. 
12mo,  Map  arid  Wood-cuts,  Muslin,  extra  gilt,  50  cents. 

This  is  a  most  interesting  book,  both  in  its  description  of  the  country  and 
inhabitants  of  Central  Asia,  and  in  its  connection  with  the  remarkable  event 
of  our  world — the  Flood.  Mount  Ararat,  which  was  ascended  by  M.  Par- 
rot, must  ever  possess  to  the  Biblical  reader  most  intense  interest,  as  the 
resting  place  of  the  ark  after  the  universal  deluge. — Pittsburgh  Chronicle. 
A  work  destined,  from  the  intrinsic  interest  of  the  subject,  and  the  full- 
ness of  detail  which  is  spread  before  the  reader,  to  a  very  wide  circulation. 
The  idea  of  ascending  Mount  Ararat  seems  to  have  risen  with  the  traveler 
to  a  passion  ;  previous  travelers  had  never  accomplished  it ;  the  natives  of 
the  region  looked  upon  it  as  impossible  ;  their  superstition  regarded  the 
inaccessible  summit  as  the  mysterious  resting  place  of  the  ark  to  this  day. 
How  Dr.  Parrot  approached  the  region,  what  adventures  he  met  with  by 
the  way,  what  manners  and  customs  he  witnessed,  how  he  twice  essayed 
to  reach  the  sacred  peak  and  turned  back,  and  how  on  a  third  attempt  he 
accomplished  the  feat  through  difficulties  the  recital  of  which  has  led  sci- 
entific men  still  to  doubt  if  the  ascent  were  really  performed — may  all  be 
read  in  this  compact  volume,  illustrated  by  maps  and  engravings,  with  every 
aid  to  the  reader's  comprehension. — News. 

Hardly  a  subject  could  have  been  selected  more  stirring  in  its  character 
than  "  A  Journey  to  Ararat."  Held  in  equal  veneration  by  Jew,  Christian, 
and  Mohammedan,  and  regarded  with  superstitious  feelings  even  by  the  pa- 
gan, that  mountain  has  always  enjoyed  a  degree  of  celebrity  denied  to  any 
other.  Sinai,  and  Horeb,  and  Tabor  may  have  excited  holier  musings;  but 
Ararat  "  the  mysterious" — Ararat,  which  human  foot  had  not  trod  after  the 
restorer  of  our  race,  and  which,  in  the  popular  opinion,  no  human  foot  would 
be  permitted  to  tread  till  the  consummation  of  all  things— Ararat  the  holy, 
which  winged  cherubim  protected  against  the  sacrilegious  approach  of  mor- 
tals, and  which  patriarchs  only  were  permitted  to  revisit,  appeared  in  many 
respects  an  object  of  curiosity  as  unique  as  it  was  exciting. — London  Athe~ 
ncEum. 

It  is  a  highly  entertaining  work,  embodying  much  historical,  geographi- 
cal, and  scientific  information,  and  conveying  a  knowledge  of  the  character, 
habits,  and  manners  of  the  people  among  whom  the  author  traveled.  The 
ascent  of  Mount  Ararat  is  so  very  difficult  that  many  persons  have  doubted 
whether  the  feat  was  accomplished  by  Dr.  Parrot,  but  his  acknowledged 
integrity  ought  to  place  his  claims  in  this  respect  above  suspicion.  The 
lovers  of  bold  adventure  will  find  in  this  volume  much  to  gratify  their  pe- 
culiar taste,  and  the  general  reader  can  hardly  fail  to  be  pleased  with  it. — 
New  York  Tribune. 

This  volume  has  claims  upon  the  public,  as  a  scientific  and  truly  valuable 
work,  which  have  been  possessed  by  few  others.  It  is,  in  fact,  the  con- 
densed narrative  of  an  exploring  expedition  sent  out  by  the  Russian  gov- 
ernment into  the  region  about  Mount  Ararat,  a  region  which  possesses 
more  interest  for  scientific  men,  perhaps,  than  any  other  in  the  world 
which  has  been  so  little  explored. — New  York  Courier. 

It  reads  more  like  the  travels  of  Von  Humboldt  than  any  book  we  have 
lately  read.  The  writer  is  a  man  of  science  and  observation,  and  the  book 
v/e  recommend  to  the  public.— Lowell  Courier. 


OF    POPULAR    STERLING    LITERATURE.  7 

IX. 

Remarkable  Criminal  Trials. 

TRANSLATED    FROM  THE  GERMAN    OF   FEUERBACH. 
BY  LADY  DUFF  GORDON. 

12mo,  Muslin,  extra  gilt,  50  cents. 

A  bock  of  thrilling  interest ;  one  that  can  not  fail  to  be  read  with  avid- 
ity.— New  York  Courier. 

This  work  abounds  with  singular  cases  of  criminal  jurisprudence  in  Ba- 
varia, of  the  most  astounding  and  thrilling  interest,  the  details  of  which  are 
of  remarkable  character,  and  differ  essentially  from  those  hitherto  familiar 
to  the  public  in  England  or  this  country.  They  are  fully  equal,  in  their 
absorbing  interest,  to  any  thing  iu  the  famous  "  Causes  Celebres"  of  France ; 
and,  perhaps,  for  their  unique  and  striking  features,  are  unexcelled  by  any 
delineations  of  crime  elsewhere  on  record. — True  Sun. 

Public  attention  was  first  drawn  to  this  work  by  an  able  and  interesting 
article  in  the  Edinburgh  Review.  They  are  all  narratives  of  marvelous  in- 
terest— more  strange  and  wonderful,  many  of  them,  than  any  work  of  fic- 
tion, and  giving  to  the  reader  a  clear  view  of  the  nature  and  peculiarities 
of  the  criminal  jurisprudence  of  Germany. — N.  Y.  Commercial  Advertiser. 

Its  illustration  of  the  many  curious  customs  of  German  criminal  jurispru- 
dence will  be  sufficiently  startling  to  the  English  reader ;  but,  apart  from 
this,  the  extraordinary  subtle  discrimination  thrown  into  the  narrative  of 
each  particular  crime  gives  to  the  volume,  as  a  mere  story  book,  the  intel- 
lectual interest,  the  passion,  and  all  the  rich  and  various  coloring  of  a  phil- 
osophical romance.  The  translation  is  excellent,  and  a  judicious  compres- 
sion of  the  original  has  added  much  to  the  effect. — London  Examiner. 

The  narratives  abound  with  thrilling  interest,  setting  forth  the  constant 
recurrence  of  crime,  detection,  and  punishment,  in  which  the  attention  of 
the  reader  is  roused  by  the  novelty  of  the  scene,  and  rewarded  by  the  light 
thrown  upon  the  darkest  portion  of  human  nature. — 2iew  Bedford  Mercury. 

This  work  has  been  so  highly  extolled  by  the  Edinburgh  Foreign  Quar- 
terly and  other  reviews,  that  not  much  need  be  said  of  its  character  and 
claims  to  public  notice.  It  presents  some  of  the  most  remarkable  stories  of 
horrible  crimes  and  their  exposure  we  have  ever  met,  and  gives  a  very  clear 
and  vivid  conception  of  the  peculiarities  of  German  criminal  jurisprudence. 
It  is  a  book  which  will  be  universally  read,  as  one  of  the  most  thrilling  and 
absorbing  interest.  The  translator  has  given  in  the  preface  a  very  good 
account  of  the  criminal  law  of  Germany,  and  has  selected  only  those  por- 
tions of  the  original  work  which  will  have  the  greatest  value  and  interest. 
— Mirror. 

This  book  is  of  an  entirely  different  character  from  works  of  a  similar  title 
that  have  hitherto  appeared.  It  contains  an  account  of  fourteen  trials  for 
murder  in  Germany,  and  the  object  of  it  is  to  show  the  peculiar  mode  of 
trial  instituted  by  the  Bavarian  code. — Evening  Gazette. 

The  records  of  crime  are  not  usually  a  profitable  kind  of  reading.  The 
contagion  of  the  example  is  generally  greater  than  the  warning  of  the  fate 
of  the  criminal ;  and  many  a  villain  has  been  made  by  the  very  means  taken 
to  keep  him  from  crime.  But  as  much  depends  on  the  manner  of  the  nar- 
rative, and  as  it  is  possible  to  extract  some  of  the  gravest  lessons  of  virtue 
and  wisdom  from  the  misdeeds  of  others,  it  gives  us  pleasure  to  state  that 
the  present  work  is  unexceptionable  in  this  respect,  while  the  cases  posses* 
extraordinary  interest,  and  are  replete  with  instruction.  They  afford  much 
insight  of  human  motives,  and  teach  impressive  lessons  of  the  retributive 
justice  of  Providence,  and  the  misery  and  evil  of  sin. —  Biblical  Repository. 


HARPERS    NEW    MISCELLANY. 
X.,  XI. 

Journal  of  Researches 

INTO  THE  NATURAL  HISTORY  AND  GEOLOGY  OF  THE 
COUNTRIES  VISITED  DURING  THE  VOYAGE  OF  H. 
M.  S.  BEAGLE  ROUND  THE  WORLD. 

BY    CHARLES    DARWIN,    M.A.,    F.R.S. 

2  vols.  12mo,  Muslin,  extra  gilt,  $1  00. 

This  is  another  most  valuable  contribution  to  the  cause  of  popular  educa- 
tion, issued  in  Harper's  New  Miscellany;  a  series  that  bids  fair  to  surpass 
even  their  Family  Library  in  the  sterling  excellence  and  popularity  of  the 
works  which  it  renders  accessible  to  all  classes  of  the  community.  The 
work  contains,  in  a  condensed  and  popularized  form,  the  results  of  the  Brit- 
ish Exploring-  Expedition,  which  Mr.  Darwin  accompanied  at  the  special 
instance  of  the  lords  of  the  Admiralty.  The  voyage  consumed  several 
years,  and  was  performed  at  a  very  heavy  expense  on  the  part  of  the  Brit- 
ish government.  Yet  here  we  have  its  most  important  results,  divested  of 
all  scientific  technicalities,  and  presented  in  a  form  at  once  attractive  and 
accurate.  The  work  is  entitled  to  secure  a  very  wide  circulation.  It  con- 
tains an  immense  amount  of  information  concerning  the  natural  history  of 
the  whole  world,  and  is  superior,  in  point  of  interest,  and  value,  to  any  simi- 
lar work  ever  published. — Neiv  Yerk  True  Sun. 

A  work  very  neatly  issued,  and  has  the  interest  of  a  leading  subject  well 
developed,  the  unfailing  secret  of  producing  a  book  of  character.  In  the 
present  state  of  the  world,  when  new  countries  are  opening  every  day  to 
the  great  conqueror,  Commerce,  such  publications  are  of  unusual  import- 
ance. Perhaps  no  information,  just  now,  can  be  of  more  consequence  to  us 
than  that  which  puts  us  in  possession  of  the  movements  of  English  discov- 
ery.— News. 

This  is  a  most  valuable  and  a  most  interesting  work ;  one  which  com- 
bines true  scientific  worth  with  the  graces  of  style  suited  to  render  it  pop- 
ular, better  than  almost  any  similar  work  which  has  recently  come  under 
our  notice.  The  voyage  of  the  Beagle  was,  in  truth,  a  scientific  exploring 
expedition ;  and  Mr.  Darwin  accompanied  it  at  the  special  request  of  the 
lords  of  the  Admiralty.  Its  results  have  been  published  in  several  very 
elaborate,  extensive,  and  costly  volumes  in  England  ;  but  as  these  were  en- 
tirely beyond  the  reach  of  the  great  mass  of  the  reading  public,  Mr.  Dar- 
win prepared  these  volumes,  in  which  all  the  important  results  of  the  ex- 
pedition are  fully,  clearly,  and  distinctly  presented,  interwoven  with  a  most 
entertaining  narrative  of  personal  incident  and  adventure. — N.  Y.  Courier. 

This  is  a  work  of  remarkable  interest  and  value.  The  author,  in  circum- 
navigating the  world,  under  commission  of  the  British  government,  for  sci- 
entific and  exploring  purposes,  visited  nearly  every  country  on  the  globe, 
and  preserved  in  this  brief,  simple,  but  beautiful  narrative  all  the  singular 
facts  of  a  scientific,  social,  or  geographical  nature  which  are  of  general  in- 
terest. The  amount  of  information  condensed  in  these  volumes  is  incred- 
ible ;  and  the  skill  with  which  the  useful  and  interesting  is  selected  from 
that  which  is  unimportant  or  well  known  is  admirable.  We  admire  the 
style,  the  straightforward  sincerity  of  the  writer,  the  apparent  candor,  and 
the  erudite  research  which  he  uniformly  exhibits.  Without  one  quarter 
of  the  bulk  or  pretension  of  our  famous  exploring  expedition,  the  present 
work  is  hardly  inferior  to  it  in  value  and  interest.  This  series  is  gaining  n 
fine  character,  of  which  we  hope  the  publishers  will  be  jealous, — New  York 
Evangelist, 


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